If it's legal in your area, FMJ will do the least amount of damage to the pelt of any of the .30 caliber bullets out there.
If you can handload, you might check out some reduced loads using a lead bullet or one of the lighter (100 - 110 grain) jacketed bullets out there. Reduced loads may limit your range a little bit, and will probably require a sight adjustment from your normal setting. Shot placement would be the most important thing in taking down a coyote anyway.
There are lighter (85-90 grain) .30 Caliber bullets out there, but they're designed with things like the 7.62x25mm Tokarev and other pistol-like cartridges in mind. Again, reduced loads may be your friend with these.