What Chinbunny says is generally regarded as the indisputable word when it comes to chickens and rabbits, but due to my set-up I have had to try some different things.
Through trial and error, I have discovered that:
1) Rabbits can and do just fine living in a colony setting in the chicken yard. You're biggest issue will probably be dig outs. I deal with this by having a large dog that patrols the perimeter every time she is let out and she reminds the bunnies where they are safe. I have also reinforced certain areas that were especially tempting to the curious bunny. The girls have a warren dug under a plywood platform and are able to snuggle up and stay warm and dry. More so, I would say, than the rabbits in the cages.
2) Depending on what you feed your animals, you may not have an issue with keeping your bunny healthy from a dietary perspective. Currently, my yard rabbits are by far my best conditioned animals. They get their pellets in a bowl hidden from the chickens, but also eat the grains, BOSS and calf manna I feed as treats to the chickens. I feed my chickens whole grains, kelp and fish meal. Fish meal is the only thing that wouldn't be good for the rabbits, but they are utterly disinterested in it, so no worries.
3) SOME rabbits will be especially susceptible to the dust that chickens kick up. This is by far your biggest concern. Even though my set-up is open on two sides, my Thriantas still get allergic reactions and I am trying to figure out a way to move them away from the chickens. The Flemish Giant and Silver Fox on the ground show no symptoms, nor did the Rex rabbits when they were the yard bunnies.
Basically, I feel like the colony method of keeping rabbits and chickens is better than keeping cages above the chickens. If you do that, you have to worry about chickens kicking up dust and the rabbit having no way to get away from it, and you also have to find a way to prevent the chickens from roosting on the cages. The free range yard rabbits are so much easier.
As for coccidia, I have heard mixed reports. I was very worried about it, but I check my rabbits frequently, handle them daily, and they are fat and sassy, NO symptoms of illness, no dirt or poo on their feet. I don't know, but it may have something to do with the fact that I keep ACV in all the water. It might also have to do with the fact that I have heard from several reputable sources that coccidia strains are species specific.