I was taught that a coyote is no different than a rattlesnake or a rabid skunk or coon--you plumb always kill 'em. When you've had newborn calves killed by coyotes, henhouses raided, and small dogs and cats disappear to coyotes, you learn to loathe them with every fiber in your body.
In the cities and larger towns, you're at the mercy of some rather idiotic laws contrived by city people whose only callouses on their hands came from playing golf. If I were to hit a coyote in town, I'd simply back up and run over him again to kill him. Much as I despise them (coyotes), I despise needless suffering even more.
In the country when we see a coyote ambling across a field or pasture, if I can take the shot safely (no livestock or houses behind the target), I'll take the shot. Where I come from in West Texas, you're doing everyone around--especially the ranchers and farmers--a huge favor. I've yet to see or even hear of law enforcement being called because someone was pulled over on the side of the road taking a shot at a coyote. Local dispatcher would probably just assume the caller was a big city yankee from Boston or someplace.
JD