I shoot a lot of different shotguns on coyotes, 16 and 12ga with 2 1/2 to 3 inch chambers mostly with 1oz or 1 1/4oz of NP BB's.
To me the very most important things a with a coyote shotgun is FIT. When the shotgun hits your shoulder your eye needs to be on the sights, if you have to Bob your head around to get lined up you are wasting time or will take the shot before you should.
Knowing how you shotgun shoots is very important also even with the light loads I use I rarely lose a shotgun coyote because I know the limits of my load and stay within those limitations.
Most of my shotguns are combo guns so I don't have to try and stretch them for long shots.