X2 on see if you can figure out where they are living, if under the coop see if you can block access. If you can keep a clear area around the coop so they have to cross open space to get there, it helps.
Those 5 gallon bucket traps, I just use the bucket and a couple of 2-3 inch wide boards about two feet long that stick a couple of inches over the top of the bucket. I've found they work best when the bucket is up against a wall with the boards against the wall going up to the bucket. Water to about three inches from the top, and bait with a layer of sunflower seeds, some seeds making a trail up the boards helps also. I've tried the various soup can they jump on type things, and the sunflower seeds really seem to work just as well. Just feed the contents, mice and all, to the chickens in the morning and rebait the trap at night.
If you don't want to go with snap traps, electronic traps like the RatZapper work, really like those for inside use.