Trees in chicken run. what can I grow around them?

Some background.
I remember reading about a gardener who followed his vegetable growing in beds with chickens to clear up and manure the bed for the next crop.
He planted something that was able to grow and deal with the hot chicken manure much better than most plants. I've searched but my google-fu is letting me down.

My situation
There is a young apple tree right where we want one of the chicken runs, As well as fencing around the tree, I'd like to plant something around it to soak up as much excess nitrogen as possible. I'll also be putting down sawdust inside the fencing.

Does anybody have any suggestions for plants that will help the tree deal with the nitrogen loading. I realise I'll probably loose the tree in the long term, but If I plant another now, and baby this one along for a few years I'll get a nice crossover, rather than a dead tree and waiting for a new one to bear.

Rus

Apples and pears may be the worst things to expose to chicken manure. They grow too fast and the new growth is more susceptible to fire blight. I think chicken manure was probably  a main factor in the loss of two apple and two pear trees in my back yard. I was using a chicken tractor but the yard was all fruit trees and too small to handle that much nitrogen.  I moved the chickens to another part of my yard and replanted. I let the chickens roam the orchard some, but they are off it most the time. They have a big area for just 4 chickens.

Planting something to use the nitrogen might help. If there's not too much shade and there's plenty of water, corn uses more nitrogen than most plants do. Just mowing grass and bagging the clippings would help some.

I would put the chickens somewhere else if possible though.

You could plant, leguminous plants like Mung beans.

Legumes add nitrogen.

Comfrey.

Comfrey is a nitrogen pig, it's roots drop pretty much straight down into the soil to mine nutrients so it doesn't compete with apple trees in the same soil profile, chickens love it, and it's hardy as all heck once established.

I plant my vines in and among my fruit trees: pumpkins, various squash, watermelon, tomatoes, cucumbers, and the like.  Once they've fruited, I'll let the girls in to tear them to pieces.

Regardless of what you plant, you'll need to fence the girls out while things are growing and establishing themselves or they'll rip everything out.  Our growing season is 12 months a year here, so I can keep them out for 3 or 4 months, turn them loose afterwards and they'll prepare the soil for the next crop cycle.  But I've seen them destroy a full-grown 3 lb. cabbage in minutes.  They dig up my ginger if I don't watch where I put them.  They'll pull half-grown carrots right out of the ground.  Chickens are the cutest little vandals you ever saw.

But in the fall, they are my little clean team.  I'll let them take the first pass through the orchard for a couple of weeks and they clean up all the fruit fall and move all the mulch around for me.  Then after I've pulled all the spent summer veggies and piled them up, the girls will rip through that pile and continue to make a mulch of all those dead vines.  Then the vines go into the compost pile, and the girls go back through the orchard again, this time digging and scratching in earnest to find all the best worms that have been growing fat all summer.

I'll pull them off and fence them out, and the winter crops go in ---- either cover crops or peas, carrots, brassicas and the like.  Around March or so, the girls get to go back in and do their work again for a month or more.  

I still have to fence off the ginger and other plants that are growing throughout the year, but if you manage the girls right, they are wonderful, and they dump their poop on the orchard at the right time -- fall and spring.  I agree -- I'd be careful with putting too much nitrogen rich chicken poop down in the heart of the summer growing season.

What about filling the area with as many carbon sources as you can get your hands on?  Pile in the leaves in fall and let the chickens shred them all winter.  In spring you have compost.  That's what I'm trying to do anyway.  My chicken run is under some established apple trees to protect them from hawks.  So far I haven't been able to get all the woodchips I would like for the area but my neighbor gave me a few garbage bags of pine needles.  Hopefully it's enough to absorb the manure from four hens.

Thanks for the replies.
Moving things is not really an option, while it's rather big for the Netherlands, our garden is only 35 meters long. We're not doing too badly fitting everything in, but plans change, understanding grows and we're in the situation that we're in.

This is where they are at the moment, which is clearly not good enough, although we let them out for half the day, most days and give them green stuff also.

And this shows my tree problem

As we've only got about 450 m2 we're not able to come close to the ideal for the chickens.

I'll fence them out of the area immediately surrounding the tree, try the comfrey in this area and see how it goes.