For use on coyotes or bobcats, with a desire to be humane, this begs the question which you plan to hit him with. If it is the ball, how much difference are a few out of 25 No6 shot going to make? If it is the shot, why not forget the ball and have a lot more of them?
r
Buck and ball hasn't found much favour in large caliber shotguns for deer, in which a small number of large buckshot, the size as in a deer buckshot load, are used. It was more an early military load, and quite useful from a smoothbore in dense brush, but animals don't know to quit and report sick.
It strikes me that the best thing for the purpose intended would be to concentrate on a single ball or slug, both of which can be quite effective from a shotgun. The trouble is that most .410s are quite heavily choked, and don't allow a projectile which fits the rest of the bore closely, either due to its own diameter or use in a shot cup wad.