If you want a renewable crop which will provide them with high protein feed supplement, plant some comfrey. Be sure you buy a sterile plant, as the seeds can be invasive. check out Coe's Comfrey for low cost plants. I started some about 5 weeks ago, and was very pleased with the vigor of the plant material received. Read up on the plant before ordering any.
Perennial herbs are great for not only food, but for attracting yummy bugs and keeping bad critters away. They also have other healing properties that chickens benefit from.
I would suggest that you fence off the area you want to plant and grow, around the coop with chicken wire of some kind. If your birds are spoiled and free range like mine do, a 2 foot fence seems to work well as there's too much for them to do otherwise on the property for them to figure out how to jump the fence... which has worked here. If they're confined, you might have to go higher. I harvest from garden areas that are fenced off and let the chickens access these areas this time of year once everything dies back. The chickens are really good at scratching up any grasshopper egg casings, beetle larvae, and other things hiding among the plant crowns that I don't want.
I am considering planting some nasturtium around the edges of my run. They bloom profusely and the leaves are edible so I am figuring that it will attract a lot of insects for the chickens and also pretty up the perimeter of the run as well. Alaska is a variety with variegated leaves.