Use quality ammunition

The 3.5" Dead Coyote and Winchester 3.5" #4 lead buckshot are both heavyweights in the ammo world.  Both have 54 very lethal pellets and are a dead heat for first place. There were actually 55 pellets in the last two Winchester shells I cut apart for confirmation. Third best is 3" Dead Coyote with 51 pellets, 1 5/8 ounces of hevi-shot. There are some other T-buck tungsten loads, but after that, there are some other loads that are much less.  Realistically, anything will work, even bird shot, if the range is close enough.  However, outside of the 30 yard mark, stick with the magnum 3.5" ammo.  BB's and less are generally useless for most coyote hunting.  Coyotes are tough.  A good rule of thumb for killing coyotes - One #4 buck or Hevi-T in the head, three in the neck, or five in the body will anchor them.  At any range, always be ready to follow up with another shot or rundown a wounded animal.  When in doubt, keep shooting and start running.

Buckshot costs a lot more than bullets. Shop well. Lead #4 buck is now (01/2015) about $2.20 each. Dead Coyote is more like $5.30 per shell. PLUS shipping. You can even pay more if you don't shop around.  If cost is an issue, shoot a rifle. Rifle cartridges cost much less than shotgun shells.