Yes, a .22lr is well suited for the job. More than likely won't drop it on the spot unless you hit the CNS but we're talking vermin here right? You don't worry about a roach or rat when using poison do ya. As long as it dies I could care less if it's on the spot or 200 yards away.
Couple notes: 1) Use CCI Velocitors. Stingers don't have very good penetration (designed for small rodents) and the Velocitors effectively split the power difference between MiniMags (and similar) and the .22M. 2) For the job and ranges you are talking about don't waist money on one of the rimfire magnums. Results will only be marginally better than with the .22lr Velocitors and either will kill a coyote dead with identical shot placement. Coyote may just run a few steps less with the rimfire magnums is all.