Personally, I only shoot lead from lead only chokes. Not nickel plated lead - lead. If 00 buck is legal in your area for deer, and it patterns well for you, and you want to use buckshot instead of any of many other superior options, then it would work.

For other info on shotgunning for coyotes:

HNI Predator Hunting Reference Sub-Forum: Shotgun Loads and Chokes for Coyotes