I've had neighbours lose small dogs to coyotes. One was taken from inside the yard, 30 yards from the house, in broad daylight and with 2 adults seated at a picnic table nearby. I can't let my small dog out at night without accompanying her. I've shot two at night, on two separate occasions, as they sat on their haunches near the barn and gazed at my dog taking a crap. Legal? Don't really care! I will still shoot any coyote that comes within sight of the house if I can reach a firearm in time...and I can almost always do that! I want them to fear me, and to treat the area of my house as no-man's-land. I love hunting coyotes for sport and fur, but this isn't hunting that I am referring to here. It's predator/pest control, plain and simple.
I think that many or most of the problems that people have with coyotes are caused by the attitude of the people in question. "Live and let live" does not work when it is applied to an intelligent, predatory animal species that knows you have something it wants. "Shoot on sight" comes much closer to having the desired effect, and rest assured, you will never...ever...cause any significant damage to the local coyote population by following that path.