Checking the hunting regulations of the state you will be hunting is very sound advice.

Tennessee allows the use of BBB[.19 dia] or smaller for coyote except during big game season,rifled slugs or number 4 birdshot or smaller are then your only options.When hunting small game,with a shotgun, it is illegal to possess
shot larger than number 4 birdshot.

It appears the only legal use of buckshot in Tennessee is on feral dogs,cats and humans.

WC

My coyote set up consists of a Remington 11-87 supermag shooting 3 1/2" BB loads in Hevi Shot. I get devastating patterns out to 50 yards with a full choke.
Good luck.
Fordfreak

Ray:

Trust me, bird shot is a bad choice for yotes...

Hunting1 knows what he is talking about.

With the chicken coop as bait, and the house as a blind, and the chickens squaking as my wake up call...

I shot at coyotes with 00 buck, and the animal walked through the pattern.

As is says in 1963 "Shooter's Bible", #4 bird shot for coyotes.
Coyotes do not walk another step when hit with those duck loads.