.222 Rem is more than enough for coyotes. For saving fur, it may be the best of what you've listed with most any .224 bullet out there. I've had good luck with el cheapo` Wally World special 55 grain power points as well as much more expensive bullets.
If you're sure your max range is going to be around 250 yards, either slow the bullet down, or harden the bullet up.
Stretching the range way out there makes things more complicated as impact velocity has a lot to do with saving fur, but it sounds like that's not going to be a concern for you and your situation.
