You have several options here. Gets some gloves and a few disposable tools like flat sticks and see if you can ID any food in there, set up a wildlife camera so you can see the critter, or do the red eye nightshift and see if you can see it yourself.
Or call your local wildlife control and see if they will come out and take a look, they would know best what is in your area so even talking on the phone would help you ID it. Also they may be able to find tracks.
Setting a raked area around might help you get tracks too if your soil or area around the coop are suitable. Rake and then broom off any bare dirt so if they step there you get a good impression. They may avoid the area for a few days after that but will get used to it.