I'm not a big shotgun fan for most hunting, but I do use an 870 20 guage for foxes, and the occasional coyote that comes in on a fox calling stand.
I don't care for buckshot in any guage, but with 3" magnum #2 shot, and a full choke tube, my 20 guage rolls foxes up to 50 yards, and has reliably dropped coyotes up to 40 yards.
If you're looking for the longest reliable killing load for a shotgun against coyotes, I think you'd do better using heavy shot, instead of buckshot. Something like #2 or BB sized lead will give you denser patterns, and likely a slightly longer killing range.