Black walnut will stunt the growth or even kill tomatoes, blackberry, alfalfa, asparagus, chrysanthemum,dock, potatoes, cereal grains, pine trees and apple trees.
On the other hand, Russian olive, black raspberries, ferns, goldenrod, asters, mints, violets, wild grape, clovers, buckwheat, peach trees, pear trees, plum trees and Kentucky bluegrass all have been
found to grow fairly well either beneath or near black walnut trees 
From "Permaculture Plants for the Northeast" available online which cites the following source for that piece of information:
Kourik, R. 1986. Designing and Maintaining Your Edible Landscape Naturally.
Also, I know that toby hemenway designs a polyculture around black walnut in Gaia's Garden, I can't positively remember what plants he uses but I think black locust and mulberry were both mentioned.
Santa Rosa, California: Metamorphic Press
I really like the trees and will have quite a surplus of walnuts. I actually noticed today that I have another black walnut growing right by a bunch of apple trees and the smallest closest one is not doing well. There are 6 other huge apple trees past that so I am going to look into those buffer plants to hold off. I would hate to cut it down (plus I guess the juglone stays around for years, but It wouldnt spread anymore) but would hate more to lose the apple trees.
Ohio State University Extension Fact Sheet
Horticulture and Crop Science
2021 Coffey Rd., Columbus, Ohio 43210-1086
Black Walnut Toxicity to Plants, Humans and Horses
Richard C. Funt
The roots of Black Walnut (Juglans nigra L.) and Butternut (Juglans cinerea L.) produce a substance known as juglone (5-hydroxy-alphanapthaquinone). Persian (English or Carpathian) walnut trees are sometimes grafted onto black walnut rootstocks. Many plants such as tomato, potato, blackberry, blueberry, azalea, mountain laurel, rhododendron, red pine and apple may be injured or killed within one to two months of growth within the root zone of these trees. The toxic zone from a mature tree occurs on average in a 50 to 60 foot radius from the trunk, but can be up to 80 feet. The area affected extends outward each year as a tree enlarges. Young trees two to eight feet high can have a root diameter twice the height of the top of the tree, with susceptible plants dead within the root zone and dying at the margins.
Not all plants are sensitive to juglone. Many trees, vines, shrubs, groundcovers, annuals and perennials will grow in close proximity to a walnut tree. Certain cultivars of "resistant" species are reported to do poorly. Black walnut has been recommended for pastures on hillsides in the Ohio Valley and Appalachian mountain regions. Trees hold the soil, prevent erosion and provide shade for cattle. The beneficial effect of black walnut on pastures in encouraging the growth of Kentucky bluegrass (Poa pratensis L.) and other grasses appears to be valid as long as there is sufficient sunlight and water.
Gardeners should carefully consider the planting site for black walnut, butternut, or persian walnut seedlings grafted to black walnut rootstock, if other garden or landscape plants are to be grown within the root zone of mature trees. Persian walnut seedlings or trees grafted onto Persian walnut rootstocks do not appear to have a toxic effect on other plants.
Horses may be affected by black walnut chips or sawdust when they are used for bedding material. Close association with walnut trees while pollen is being shed (typically in May) also produce allergic symptoms in both horses and humans. The juglone toxin occurs in the leaves, bark and wood of walnut, but these contain lower concentrations than in the roots. Juglone is poorly soluble in water and does not move very far in the soil.
Walnut leaves can be composted because the toxin breaks down when exposed to air, water and bacteria. The toxic effect can be degraded in two to four weeks. In soil, breakdown may take up to two months. Black walnut leaves may be composted separately, and the finished compost tested for toxicity by planting tomato seedlings in it. Sawdust mulch, fresh sawdust or chips from street tree prunings from black walnut are not suggested for plants sensitive to juglone, such as blueberry or other plants that are sensitive to juglone. However, composting of bark for a minimum of six months provides a safe mulch even for plants sensitive to juglone.
Plants Observed Growing Under or Near Black Walnut*
Japanese Maples, Acer palmatum and its cultivars
Southern Catalpa, Catalpa bignonioides
Eastern Redbud, Cercis canadensis
Canadian Hemlock, Tsuga canadensis
Vines and Shrubs
Clematis 'Red Cardinal'
February Daphne, Daphne mezereum
Weeping Forsythia, Forsythia suspensa
Rose of Sharon, Hibiscus syriacus
Tartarian Honeysuckle, Lonicera tatarica, and most other Lonicera species
Virginia Creeper, Parthenocissus quinquefolia
** Pinxterbloom, Rhododendron periclymenoides
**'Gibraltar' and 'Balzac', Rhododendron Exbury hybrids
Multiflora Rose, Rosa multiflora
Black Raspberry, Rubus occidentalis
Arborvitaes, Thuja species
** Koreanspice Viburnum, Viburnum carlesii, and most other Viburnum species
Pot-marigold, Calendula officinalis 'Nonstop'
Begonia, fibrous cultivars
Morning Glory, Ipomoea 'Heavenly Blue'
Squashes, Melons, Beans, Carrots, Corn
Peach, Nectarine, Cherry, Plum
Prunus species Pear-Pyrus species
Bugleweed, Ajuga reptans
Hollyhock, Alcea rosea
American Wood Anemone, Anemone quinquefolia
Jack-in-the-Pulpit, Arisaema triphyllum
European Wild Ginger, Asarum europaeum
Bellflower, Campanula latifolia
**Chrysanthemum species (some)
Glory-of-the-Snow, Chionodoxa luciliae
Spring Beauty, Claytonia virginica
Dutchman's Breeches, Dicentra cucullaria
Leopard's-Bane, Doronicum species
Crested Wood Fern, Dryopteris cristata
Spanish Bluebell, Endymion hispanicus
Winter Aconite, Eranthis hyemalis
Snowdrop, Galanthus nivalis
Sweet Woodruff, Galium odoratum
Herb Robert, Geranium robertianum
Cranesbill, Geranium sanguineum
Grasses (most) Gramineae family
Jerusalem Artichoke, Helianthus tuberosus
Common Daylily, Hemerocallis 'Pluie de Feu'
Coral Bells, Heuchera x brizoides
Orange Hawkweed, Hieracium aurantiacum
Plantain-lily, Hosta fortunei 'Glauca'
Hosta undulata 'Variegata'
Common Hyacinth, Hyacinthus Orientalis 'City of Haarlem'
Virginia Waterleaf, Hydrophyllum virginianum
Siberian Iris, Iris sibirica
Balm, Monarda didyma
Wild Bergamot, M. fistulosa
Grape Hyacinth, Muscari botryoides
Sweet Cicely, Myrrhis odorata 'Yellow Cheerfulness,' 'Geranium,' 'Tete a Tete,' 'Sundial,' and 'February Gold'
Sundrops, Oenothera fruticosa
Senstitive Fern, Onoclea sensibilis
Cinnamon Fern, Osmunda cinnamomea
Peony, **Paeonia species (some)
Summer Phlox, Phlox paniculata
Mayapple, Podophyllum peltatum
Jacob's-Ladder, Polemonium reptans
Great Solomon's-Seal, Polygonatum commutatum
Polyanthus Primrose, Primula x polyantha
Lungwort, Pulmonaria species
Bloodroot, Sanguinaria canadensis
Siberian Squill, Scilla sibirica
Goldmoss Stonecrop, Sedum acre
Showy Sedum, Sedum spectabile
Lamb's-Ear, Stachys byzantina
Spiderwort, Tradescantia virginiana
Nodding Trillium, Trillium cernuum
White Wake-Robin, Trillium grandiflorum
Tulipa Darwin 'White Valcano' and 'Cum Laude,' Parrot 'Blue Parrot,' Greigii 'Toronto'
Big Merrybells, Uvularia grandiflora
Canada Violet, Viola canadensis
Horned Violet, Viola cornuta
Woolly Blue Violet, Viola sororia
*These are based upon observations and not from clinical tests.
**Cultivars of some species may do poorly.
Plants That Do Not Grow Within 50 Feet of Drip Line of Black Walnut
Colorado Columbine, Aquilegia caerulea
Wild Columbine, Aquilegia canadensis
Asparagus, Asparagus offinalis
*Chrysanthemum Chrysanthumum species (some)
Lilies, Lilium species (particularly the Asian hybrids)
Alfalfa, Medicago sativa
Buttercup, Narcissus 'John Evelyn,' 'Unsurpassable' 'King Alfred' and 'Ice Follies'
Peonies, *Paeonia species (some)
Rhubarb, Rheum rhabarbarum
Silver Maple, Acer saccharinum
European Alder, Alnus glutinosa
White Birches, Betula species
Northern Hackberry, Celtis occidentalis
Apples and Crabapples, Malus species
Norway Spruce, Picea abies
Mugo Pine, Pinus mugo
Red Pine, Pinus resinosa
Eastern White Pine, Pinus strobus
Basswood, Tilia heterophylla
Red Chokeberry, Aronia arbutifolia
Mountain Laurels, Kalmia species
Privet, Ligustrum species
Amur Honeysuckle, Lonicera maackii
Brush Cinquefoil, Potentilla species
Rhododendrons and Azaleas, **Rhododendron species (most)
Blackberry, Rubus allegheniensis
Lilacs, Syringa species and cultivars
Yew, Taxus species
Blueberry, Vaccinium corymbosum
*Viburnum plicatum tomentosum 'Mariesii'
Annuals and Vegetables Transplants
Cabbage, Brassica oleracea capitata
Peppers, Capsicum species (some)
Tomatoes, Lycopersicon esculentum
Flowering Tobacco, Nicotiana alata
Petunia species and cultivars
Eggplant, Solanum melongena
Potato, Solanum tuberosum
double-flowered cole vegetables
*Cultivars of some species may survive but will do poorly.
The authors express their appreciation to Drs. M. Scott Biggs, Department of Horticulture and Crop Science, and Harry Hoitink, Department of Plant Pathology, for their review and additional comments.
All educational programs conducted by Ohio State University Extension are available to clientele on a nondiscriminatory basis without regard to race, color, creed, religion, sexual orientation, national origin, gender, age, disability or Vietnam-era veteran status.
Keith L. Smith, Associate Vice President for Ag. Adm. and Director, OSU Extension.
TDD No. 800-589-8292 (Ohio only) or 614-292-1868
what our permie teachers told us is that the juglone does effect some plants but not all, and some might even have advantages growing near to a walnut.
one of the families that is supposed to have advantages is the nightshade family since the juglons apparently fights back the phytoptera disease.
so i was surprised to read:
plants such as tomato, potato, blackberry, blueberry, azalea, mountain laurel, rhododendron, red pine and apple may be injured or killed within one to two months of growth within the root zone of these trees.
but then again, there are not many black walnuts around in europe, mostly juglons regia, which gives way less juglons to its surroundings.
Raised beds and added organic matter help a lot. I bet the mulberry trees do too.
If that doesn't work, there are plenty of lovely flowers, understory plants/shrubs/trees including native fruits, nuts, and veggies that will grow with black walnut. Once you let go of your agenda and start thinking like a walnut, you'll be amazed as to what an incredible forest you can create.
They DO like lots of companions; they're just specific, which is not necessarily a bad thing.
Jimbo Mathews wrote:Finding this makes me feel much much better about my dismal tomato crop, as they were planted pretty close to a bit black walnut tree. What is a REAL mystery to me however is my crop of golden giant grain amaranth. The ones that are by far the tallest and best (7 ft now) are the ones most directly in line with the root radius of another black walnut tree. Maybe its coincidence, maybe weeds were suppressed and the lawn I busted up to plant these was somehow conserving nutrients better than the grass outside the radius of said walnut tree. It'll be really interesting if I can replicate this, or if similar results happen with my wicked late crop of corn in the same area. Any ideas on some possible symbiosis here?
Pigweed (which is an amaranth) grows quite well here under black walnuts. I suspect this is a plant that isn't much bothered by juglone.