You could as long as you don't have any other animals that could get inside the trap. If you really need to secure them you could put them inside in a bucket with a lid or something like that
Probably not coyotes but foxes are a different story. They are very sneaky so you never know with them. If you have a secondary coop I would put them in there.
Watch for predators (specifcally raccoons, coyotes, or foxes) and if you hear anything or see anything try to shoot it or scare it so badly that it will never come back. Once it has had a taste of chicken it is going to be back