We shoot racoons in the butt with a pellet gun to protect our kitties and their food, but are reluctant to actually kill one because it would be such a mess to bury. And if you want to eat them, don't you have to soak them in milk to sweeten the meat?
Or a .22 rimfire. My uncle bought one solely for turkey season. Coyotes scared turkeys he was calling in. He wondered why the turkeys just took off. He then saw a coyote go after it, and it was out of shotgun range.
I thought I saw two when I was hunting a year and a half ago. It was dark and 2 sets of eyes about 40 feet away were staring me down. I couldn't tell what animals they were though. I had my rifle pointed at them. If I knew for a fact they were coyotes....BOOM!. I needed to know my target though.