I use everything I own on coyotes from shotguns, and 17HMR up to .45-70. All the muzzleloaders and handguns too. I want dead coyotes. If I can salvage the pelt, fine. If not, objective is still accomplished. The PETA people should be made to watch wolves and yotes eating a deer alive. Perhaps they'd have second thoughts on the humanity of hunting.
Neighbors of mine have a large dairy, beef, sheep operation. Lambing time and the next few weeks is the worst for coyotes. We like to go over there in the early morning and late afternoon and save lambs. They are really bold until they meet up with a V-Max. My friend, the owner, parks a sided trailer along the fence for us and it makes a perfect shooting blind.
I have a night corrale adjacent to the barn for my horses. Christmas morning, I had Coyote tracks all around the barn and inside the corrale. They came in and out under the steel gates.
Use M60s, RPGs, claymore mines.....anything......just kill coyotes.
You can tell how much I love them.
Happy New Year
Pete