I used to have a single-shot New England in .22MAG. It was a tack driver with a cheap 4X32 scope. I ordered the rifle from Wal Mart and it cost me just a few $ over 100 bucks. I could hit 2" cleaning patches consistently at 100 yards with little Winchester Supreme rounds. I actually bough the rifle for squirrels and coyotes, and it's not great for either. It explodes squirrels if you hit them in the head, and it's underkill for coyotes unless you can make a head shot.

To answer your question, yes, a .22 WMR round through a coyote's head will kill it. That being said, I would suggest getting your hands on a 12ga shotgun loaded with #4 buckshot. You will be limited to about 50 yards, but if you have to aim at a coyotes head with the .22, anything past 50 yards is going to be a long shot anyway.

Good luck on your gun search. Let us know what you end up with.

rw