At this point there is nothing you can plant as ground cover that they won't destroy if they are contained to their run. You can plant things in your run, but they'll have to be protected (wired off)...I've done that with a raspberry bush. They can have whatever grows over/out of the wire. You can build a grass box - like a raised bed w/grass planted in it and covered with hardware cloth so they can only eat what grows above the wire.
When the run is down to bare dirt, most people bring in sand - which is easy to keep clean, drains well rather than getting muddy in rain, and fun for the chickens to dust bathe in. The only chance you have to grow anything back would be if you mostly freeranged them.
