I shoot them with FMJ loads. They are cheap and everyone I have shot falls dead with a small .30 cal hole, it starches them. I don't skin them, just take them to the local fur buyer. Usually get about $20-25 for whole animal. More for the cats. He doesn't mind the hole. Really never says a word. He doesn't want you to skin them, he is the pro.
I also got in with a group of guys that run them with dogs and we communicate with radios and shoot them on the run. It is too much fun. I am beginning to like varmint hunting more than deer hunting. Plus I always learn something to help with the deer hunting and get to know the farmers.
There are so many coyotes and cats here in NE Kansas it is ridiculous. Every night, everywhere I go in the country they howl. Sounds like hundreds of them.