James B

Many use the 150 grain FMJ for varmits. If you don't need worry about the pelt, the 125 grain Noslet Ballistic tip works well too.

lefteye

Try a Winchester 180 Silvertip. They are designed to penetrate large muscle and bone, but will go straight through a coyote without blowing up. Shoot the gun you are used to. Ammo is cheaper than a barrel.