Well if you are going to use a .22lr on a coyote. The stinger or velocitor would be the only two I would consider as adaquate that I have personally fired from a .22. Most of my .22 shooting is done with standard and subsonic rounds, neither of which i consider a great coyote rounds unless shots are very, very close and as a last resort, I would never perpously go out coyote hunting with a .22lr but can't say i wouldn't take a shot on one if the conditions were perfect and thats all i had with me.
Beleive me i am all about dead coyotes too, I just like to see them dead as fast as possible after being shot. As undersirable as coyotes are in cattle farming or suburban areas I still don't want them to suffer neadlessly. I respect them as being one of the most intelligent, hardest to hunt north american game animals and no matter what coyotes do, they will never accomplish the destruction to this planet or other animals like us humans have. So as much as i love to hunt them, lets try and kill them DRT when possible.
Just my .02