Best to follow Tom Arnold's advice and leave this for local option based on prevailing local mores, local law, local sheep population, local "scares" concerned with "boudoir" pets, infants and underwgt. children. Personally, I'd think all these bravos who whistle in the dark over the prospect of a self-defense shooting with the "tried by 12 vs. carried by 6" nonsense would have little trouble with an extermination project on coyotes inside or outside the letter of the law. I don't have a bit of problem with the world of hurt that was inflicted on this particular yote; if I'd shot it I might well have some qualms as I don't have sheep, children, or easily edible pets. I'd like to think there is always at the minimum the perception of necessity and self-interest in everything we do.
jack