I don't know why you are getting so worked up about running down a coyote or two, sounds like the Supreme Court just gave the green light to chasing down a herd of elk in deep snow and gunning down the whole herd with an AK47 as long as your ancestors signed a treaty giving you the right to hunt a 150+ years ago .
I did one time run a coyote down with a tractor and killed him by dropping the loader bucket on him. He didn't suffer. I didn't have a gun or I would have shot him. I figured that if the coyote would let me drive up to him in the tractor something wasn't right and he needed killing.