I don't actively hunt anything. I'd love to get a shot at a coyote, though.
My uncle is an avid deer hunter, but he also shoots every coyote he sees. He does run a ranch with some cattle on it, so it's depredation for him anyway. He keeps his .30-06 loaded with 180 grain Nosler Ballistic Tips (same load he uses for deer) with him while he's out working. If he sees a coyote, he shoots it. He doesn't care about the hides, obviously.
Good luck with your coyote hunting.