Well Ormachek, I guess that is the way a lot of us feel.
I differ from a few of the views expressed on here, though. First, I wouldn't take a head shot. One hit in the lungs and it will die quite quickly. Trying for a head shot just creates a huge danger of giving the animal a miserable wound.
For ammunition I would take ordinary, run of the mill, long rifle. For many years we had the choice of Dominion Super Clean for regular speed, or Dominion Whiz Bang for high speed, about 200 feet per second faster. For coyotes, of course, it would be Whiz Bang, but not sure what todays similar loadings would be.
Edited to say I didn't see the posting of Rookie Wildcat before I posted. People like he will be sure of the shot before they take it and will likely make a clean kill on a head shot. I was thinking of the average person out there with a 22 when a coyote appears.