Unless you are keeping the hides, there's no such thing as overkill. If you are keeping the hides, a .222 or .223 would work better. But if you use a solidly constructed bullet like you would use for deer, you can still probably salvage most hides with a .25-06. May have to do a little stitching and may ruin a few, but that's just a price you pay to coyote hunt with a deer rifle.