I use a 22 Hornet, 222remmag and a 243Win for coyotes, all are useful in their own right. However, if I had to pick just one, it would be the 243Win.
You can shoot a 55gr 6mm bullet to around 4,000fps, something very few 22's can do. Then, when the winds pick up, or the ranges get long, I can use a 100 or 105gr bullet, and fold them up nicely at 400yds+.