Take a ziplock bag, a table fork, and poke the bag once, so ya have 4 about 1/8 inch holes in the baggie. Put a slice of bread in the bag, pour a few teaspoons of Vanilla extract on the bread. Coons and opossums can't resist it, I've even caught the occasional fox (quite rare in that area I lived at the time) with this bait, and it isn't as messy as other stuff. We didn't have Coyotes where I used to trap, I suppose I'll have to try it and see if it works as well. Did lure Fox so I'm guessing coyotes might be attracted too. We haven't had a problem with coyotes so far even though we have'em, I think probably because I "mark" a perimeter around the property. How do I mark it? Ehh . . . . a few beers help, if that gives ya an idea.
If ya get a trap shy critter, covering the box trap with debris or a gillie cloth can putt'em at ease a bit too. (be careful not to interfere with the mechanism though) If you have a double-end trap, try leaving one end closed too. Trap-savvy coons will do a fast "run through" and steal the bait and be out the other side before it even closes. A good reason to secure the bait too.
If you're handy, and you have something killing the chickens themselves . . . they like nothing better than a "lone chicken" roped off from the flock. It's not that difficult to modify a store bought box trap to use a live chicken as bait with a divider that keeps the chicken from getting nabbed. The most effective thing is a well placed piece of lead, administered at high velocity.
Good luck with the critter control