My family shoots .233, .204 (my preference), and .22-250 for prairie dogs, but .243, .243 wssm, and .22-250 for coyotes. We are not too concerned with the pelts. We just shoot them as our neighbor farmers ask us to.
I would love to try the .220 Swift next. I have heard nothing but good about that round!
I am no pro, just an enthusiast.
Victor