If You use Buck-shot in the shotgun it was make a good close-in shot on Coyotes and Foxes.Personally I would use a .243,.223 or go a little smaller with a .220 Swift,.22 Hornet or a .204 for Varmint Hunting.I use my Browning bolt-action .243 Rifle,my Buddy just bought a Savage Axis in .223 and my other Predator Hunting Partner uses the .22 Hornet in a Ruger bolt-action Rifle.Some guys use a .22 magnum for Foxes,Bobcats and Coyotes.Another popular Varmint Rifle is the 22-250,its a faster bullet that shots further out for using in more open area's.