Anyone who thinks a 22lr can't or shouldn't be used to kill a coyote is out to lunch. I've killed many around the farm with one.
Some drop in their tracks. Some run off and find somewhere to pile up and die. But in the end if you hit vitals you have a dead yote.
I shot one just last weekend with the 22lr. It was early morning and I was going out to shoot a coon that I saw run into the shed. When I came back out of the house from grabbing the .22 I spotted a coyote coming across the field in the direction of the buildings (they come by looking for cats).
I circled around the back side of the shed where it couldn't see me and waited. He came within about 75 yards, must have smelled me there and turned the other direction. I let out a yelp and when he stopped and turned back to look I shot it.
I knew it was a good hit because he turned and took a couple bites at his side then took off over the hill stumbling a few times.
I waited it out for about an hour and then went and followed the tracks in the snow. There were two more spots with blood in the snow where it had stopped and messed around before the tracks entered the bush.
I found him about 20 feet inside the edge of the bush piled up beside some thick brush dead as can be. Entrance hole in his lungs. Where it died was about 275 yards from where I shot it.
If you hit vitals the yote may run off but it isn't going to go far.
If you don't hit vitals I don't care what caliber of firearm you used to shoot it, you're going to end up with an injured coyote running around for a long time.
Yes, I think there are more effective caliber choices for coyote. If I'm actually out hunting for them my main rifle is a 25-06. But for close range pest control the .22lr is perfectly capable of doing what you need it to do.
Close range + hit vitals = dead yote.