Rifle: Just about any rifle will do the trick for coyotes.
These dogs are smaller sized than 1 may think with, with a 30 pounder becoming a large 1. They are also soft skinned, so a large bullet is not essential and will ruin the hide much worse than a smaller sized 1. My personal viewpoint is that a 243 caliber rifle is the perfect coyote rifle.
It is flat and fast shooting, with sufficient weight to carry the bullet for lengthier distance capturing.