Humane as in, does not kill the mouse? If you don't kill it what will you do with it? It may seem mean but I'd exterminate as many as I possibly could. If you think you have 50 mice in your coop it's probably many times that number and they reproduce like crazy. They can spread disease not to mention consume a whole lot of feed. I'd not be wanting to spend $$ on chicken feed just for the mice!
I would set traps and keep setting them, all over the place. Try a bucket trap. Fill it half up with water and float bird seed or sunflower seeds on the water so it looks solid. Mice/rats get in and can't get out. If you have bazillions of mice you may have to resort to putting out bait in tin cat traps. I dislike doing that but I had to do that once to get control of a mouse problem. I checked all around every morning before the chickens came off the roost and again in the evening. Never found any mice laying around but I did solve the problem and it hasn't happened again.
I would set traps and keep setting them, all over the place. Try a bucket trap. Fill it half up with water and float bird seed or sunflower seeds on the water so it looks solid. Mice/rats get in and can't get out. If you have bazillions of mice you may have to resort to putting out bait in tin cat traps. I dislike doing that but I had to do that once to get control of a mouse problem. I checked all around every morning before the chickens came off the roost and again in the evening. Never found any mice laying around but I did solve the problem and it hasn't happened again.