OK, my opinion is so very different from all of previously posted so I'll throw it out to ya'll:
My Dads uncle hunted coyotes his whole life (he lived to 92). He was the local expert and could tell ya WAY more than you ever wanted to know about coyotes and their habits. He also raised sheep. Lambed in the pasture. Not a lot, but a pasture, with trees and ditches.
His theory...never shoot a coyote UNLESS that specific coyote is giving you problems (shoot the cat killing coyote, but not an innocent one just walking by). Why? Because coyotes are VERY territorial. They will defend their area against all other coyotes. So, if "your" pack of coyotes don't kill sheep, cattle, cats, whatever, then they probably won't start to kill that animal. But, if you shoot and remove the "nice' pack, a new pack WILL move in and they might be the livestock killing kind. So, be selective in which one you shoot.
And don't worry about stray bullets....as the city folks that come to the country to hunt deer and turkey never seem to worry about which direction they are shooting, so I am sure they won't mind a hole in THEIR house, vehicle, pet, etc... (please note sarcasm in the past paragraph...although it is not said with a smile.) ???