I can NOT recommend anything rimfire, for coyotes. Coyotes are tough customers and can take a lot of punishment/bullets and not die. At that point all you've done is educate it for the next person. Rest assured, you will not see that coyote again, as it may not leave the area, but will become nocturnal.
I agree with this all the way, it sure holds true with our coyotes here in Missouri.
While deer hunting one year I shot one with a 280, the bullet entered his chest, blew a exit hole bigger then my fist, stringing his intestines to where he was stepping on them.
He started spinning then took off running, stopped broadside to look at me about 250 yards out, another shot finished the job.