Even when you have a proven coyote killing shotgun load it is pretty easy to NOT center the pattern on the coyote so be ready to shoot the coyote again if it is still moving.
When I first started calling coyotes and was shooting them with a shotgun I used 3" 12 ga goose loads that I had.
I had Federal Premium 3" 1-7/8 oz loads of copper coated lead #2 and size BB. It didn't take long to see that the copper coated lead #2 shot did NOT work nearly as good as the copper coated lead BBs did on the coyotes. If the coyotes were not facing me the lead #2 shot was not big enough or heavy to penetrate deep and or break bones nearly as good as the copper coated lead BB shot did.
I don't shoot at coyotes over 40 yards away very often so I like the Federal 1-7/8 oz load of copper coated BB loads with 98 pellets per shell over the 3" number 4 buck shot loads with only 41 pellets per shell.
Now I live and hunt in an area where I have to use lead free shot to hunt coyotes. The denser than lead loads that are 12g/cc like Winchester Xtended Range, Remington Wingmaster HD and Hevi-Shot Goose loads in size #2 and bigger are very good coyote loads. All of these types of shot are denser than lead and much harder than lead so they don't slow down as fast as lead, they break bones better than lead and penetrate much deeper than lead. So the denser than lead 12g/cc #2 shot actually works pretty good on coyotes. But I prefer size BB in the 12g/cc denser than lead shot.
I have dropped many coyotes running away from me at 40 yards with Remington Wingmaster HD BB shot, it really breaks them down. They may need to be shot again but they don't get away. I want big enough and heavy enough shot to drop a coyote between 40 and 50 yards no matter what the shot angle is.
A good pattern doesn't do any good if the shot is not, heavy enough and hard enough to penetrate deep and break bones. I don't want to use a coyote shotgun load that requires head shots, coyotes are not turkeys.
The Federal Heavyweight Coyote loads have 15g/cc BB shot in them. The 12g/cc shot is 10% denser than lead, the Federal Heavyweight shot is 35% denser than lead so it out performs Hevi-Shot Dead Coyote T shot by quite a bit at longer ranges. The 3" Federal Heavyweight BB loads have 12 more pellets per shell than the Hevi-Shot 3" T shot loads have. Both of these loads are pretty expensive but I would go with the Federal Coyote BB load because of the 12 more pellets and denser shot.
Federal no longer makes the Federal Heavyweight #2 shot waterfowl loads but if you can find any they work great on coyotes.
I bought 5 cases of the Federal Heavyweight 3" 1450 fps #2 shot 1-1/4 oz loads when they were being closed out. I took the shot out of all of them and reloaded 3" 1-1/2 oz loads with the Federal Heavyweight #2 shot in them. Each shell has 90 pellets in them and they are devastating on coyotes.
I just ran some loads in my Shotgun Shell Ballistic calculator. These numbers are pretty crazy on the denser than lead shot especially the Heavyweight 15g/cc shot.
All of these loads are at 1300 fps and I had 3" of gel penetration entered. They say 2.50" of gel penetration is needed for geese.
I am not saying 3.0" of gel penetration is good enough for coyotes but these numbers will really show the differences in penetration in the shot sizes and the pellet densities.
#4 lead shot at 1300 fps got 3.0 " of gel penetration at 20.7 yards
#4 WIN XR 12g/cc shot at 1300 fps got 3.0 " of gel penetration at 31.2 yards
#2 WIN XR 12g/cc shot at 1300 fps got 3.16 " of gel penetration at 47.7 yards
BB shot Rem HD 12g/cc shot at 1300 fps got 3.26 " of gel penetration at 80 yards
#2 Fed HW 15g/cc shot at 1300 fps got 3.26 " of gel penetration at 88.7 yards
BB shot Fed HW 15g/cc shot at 1300 fps got 3.26 " of gel penetration at 137.9 yards
Look at the differences in the 12g/cc loads of BB, #2 and #4 shot.
Its to bad Federal didn't make a Heavyweight Coyote load with #1 or #2 shot!