Out here in Southern California we have an approach that is quite workable.
It's called the "three S": shoot, shovel, and shut up.
One resident used it against a mountain lion (cougar, far more dangerous than a hungry coyote) that was entering his yard and threatening his children.
Gotta be some Arizonans who feel the same way.
When used correctly that is the best applicatiion of theory.
We live near a mountain preserve in North Phoenix. Recently, my wife was out walking our boxer dog and watched 2 coyotes saunter down into the neighborhood not far in front of her and our dog. She was about to go down the same street, her usual route, when she looked up into the mountain preserve and saw a third coyote watching. She and the dog turned around and high-tailed it home.
Since we live in a residential neighborhood, we can’t really get away with shooting them. If several coyotes were physically attacking the dog and a couple of shots were fired the cops might or might not let you off without charging you — you know how that goes. But we sure can’t get away with shooting them to thin the herd, though we would really like to.
.22 subsonic works well for urban varmint control.