Black plastic in what manner? Like, shrink-wrapping the stumps? Or more loosely covering a whole area?
Actually, when I think about it either way I think this would be more trouble than it's worth. Wrapping the stumps seems labor intensive and probably not very effective, b/c the buckthorn will just put up new suckers from the ground. Covering a larger area with plastic will indiscriminately suppress all plants, not just your problem plants, and unless it is permeable it will collect
water and become a mosquito breeding ground.
From personal
experience, I would recommend against even the permeable "landscape fabric" in a setting with trees. I used this some years ago to surround strawberries and tomatoes near a mulberry tree. Some strong weeds still grew up under the fabric, and even more frustrating fallen mulberries, twigs, leaves, and other detritus built up on top of the fabric and weeds srpouted in this "mulch." Then of
course the plastic degrades after a year or so and you get scraps of plastic blowing everywhere.