From what I've read, the most common gun used in Coyote hunting is a 22-250. Honestly... I currently use my 30-40 Krag. (I know I know... too much rifle)
I have a good friend in Texas who hunts them for a living and highly recommends the 22-250 with a decent scope, but also feels that any rifle will do the job so logn as you are comfortable with it.