I've only shot 1 with a 22LR and it didn't end well.  Was about 30yrs ago and it was a 40yd shot.  Hit it right behind the front shoulder.  Yote lopped off and I don't know what ever happen to it.  
Do I think a 22LR will kill a coyote, sure.  Do I think it's the right choice, only under certain circumstances.