Coyotes are common around here. They are great rodent killers and don't bother much that I've noticed. They used to get an occasional duck when I had them around to control slugs and snails, but no loss. I finally did the last of the ducks in when they found the dog food and started crapping all over the porch. The ducks managed to over populate in spite of eagles, hawks, owls, and coyotes. And they weren't fenced, either.
I have no affinity towards cats, no special interest in them one way or the other, actually. I view them as wanton killers and of no special use. I have a couple of neighbors who are cat lovers, one of which would shoot the coyotes, the other has a "they're on their own" attitude. Guess which one I get along with?