in your question you ask if a .22 or .17 is best if you comparethe .17 to a .22wmr its faster with little ftlbs i have shoot a .17 many times and find it to be very accurate with my ruger bolt action. it has taken a few rabbits and crows and that is where i stop. nothing bigger !!! as far as coyotes i would be very surprised if it would make a humane kill on them at any range