Don't skip out on patterning your shotgun on paper. This will help YOU decide what the effective range is of the choke/shot combo of YOUR shotgun. Don't just assume that 4buck will kill a coyote cleanly at 60 yards. If the shot doesn't pattern well, OR if your shotgun patterns slightly high/low, or slightly left/right, killing a coyote past 40 yards might not be a reasonable task.
Also, the larger shot shells, such as 00 buck, or T, for instance, don't ahve very many pellets. If the pattern isn't tight, then30 or 40 yards may be the effective range of your shotgun.
I knowseveral guys thatuse copper plated BB 3", because these throw a much tighter and fuller pattern than the 4buck out of thier shotguns.