I have used a .22 mag does the job but hunt in the east .Also have used a 30/06 do not care about hide just want to get rid of the bastards.Now use 5.56 with dog town bullets mainly because it is cheaper than 30/06 and easy to carry with sing point sling and also have rails for night hunting lighting .
I've shot a couple with my 10/22 I live in an area with a bunch of 80 acre dairy farms and just drive around with a spotlight at night..22 with a bull is way quieter than my center fire which makes ir nice to use while farmers are sleeping ( I do have permission to shoot). I always used American eagle bulk pack but am liking the velociters more. That all said I would get a marlin 917 bull barrel. It's one of the most accurate guns I've ever had not much louder than the .22lr if you get the bull barrel version and way flatter shooting than the .22, wish I wouldn't have sold it. Oh and they run about the same price as a the basic10./22.
My neighbor has killed 6 or 7 yotes the past year with his 22LR. We have a coyote problem here and I appreciate every one he hits because I'm tired of losing livestock. He's probably hit 4 or 5 more that ran off and I don't care if they don't drop dead on the spot or run off. I don't think the ones that were hit will come back. They suffer much less than my butchered goats did.
All his hits have been anywhere from 65-110 yards. The CCI Velocitors seem to be an accurate fast 40g round at about 1435 fps. Do not get the CCI Stingers. Very inacurate.
So a larger or faster caliber round would put them down faster and more often, but I don't care anymore. Not at all inhumane to me. I would shoot them with a pellet gun if that's all I had at the time. Have fun.
Stingers are the best .22LR ammo for fox and/or coyotes... they ARE NOT for use in a Ruger 10-22 as is clearly stated in the CURRENT Ruger owners manual. This is due to the Stinger casing being .010 longer than a standard .22LR case. A simple solution is to have your Gunsmith deepen your chamber .012 and thereafter ONLY use Stingers. Be aware the design of the bullet gives fits with feeding reliability. They are worth the effort though when you get it right. Keep your shots under 150 yards, go for head shots and be ready for a quick follow-up shot. Keep your powder dry.