A bolt action rifle with a caliber in the range of .223 to .250 is an excellent varmint rifle. These calibers are strong enough to take down coyotes, foxes and wolverines. Savage Axis makes a very affordable and effective varmint rifle.
A semi-automatic rifle also makes an excellent varmint gun. An example of this is the AR-15 but these are not legal to own in many places. Most of these use the .223 caliber ammunition and fire at a higher rate than a bolt action, which helps guarantee a successful hunt. Another option is the versatile shotgun, such as the turkey gun or the rim fire. While these do not have the same range as a rifle, the spread of the shot makes it difficult to miss the target.