Coyotes are smart creatures, my guess is that if you were to take out a slingshot and land a couple of well placed shots they would learn and go away. Just speculatin'
Coyotes are smart. if you ping them with a marble or a rock, they'll just learn to sneak around you.
I'm not fond of senseless killing. When it comes to coyotes, rats, crows, racoons, possums, gophers, mice, any animals that thrive on humans (farming, city trash, whatever) the killing isn't- in general- senseless.
Now, there's good and bad ways to handle it. a clean shot is far better than a slow poison or starving in a trap.
As I said up above, out in the desert, far from livestock range, I'm apt to leave them alone. But I live well within the coyote's natural habitat. A lot fo responses are coming from people outside of the coyote's previous natural habitat.
Now, habitats change- and we humans are (mostly for better, but not always) agents of change. The growth of coyote habitats is soemthing we're all going to have to adjust to, but that includes killing them.
You'd be hard pressed to find anyone from a ranching family or who lived with pets and livestock in the southwest 40 years ago who would avoid varminting a coyote on their land. (even if they didn't go out looking for them to hunt.)
Very, very few of the "protect the coyotes from evil man" people have been impacted by them.
Now, I don't think they need to be eradicated, genocided, or anything, but I also don't think that's
*possible* without a genetically engineered plague.