I think that the vast majority of coyotes that I ever shot with my shotgun were 45 yards and under, old 1100 with a fixed full choke, 30" patterns at 40 yards were the norm. Running, jumping, dodging coyotes often take more than one shot. I liked F buck and #4 Buck, but killed a lot with BB, but took more shots. I shot 32 pellets of Ballistic Products #4 buck(1 5/8 oz) at 1300. Today, in my 11/87 and a Beretta 391 with extra full chokes, all pellets go in a 20" circle, and that load is a meat grinder at 50 yards.
30 years ago, my hunting partner shot a load of 28 pellets of #4 buck with 25g Unique in 2 3/4" AA hulls, buffered, RP 12 wad, 1250 fps, and he killed as many coyotes as I did. He cast his own #4 buck with Wheel Weights and added some linotype. With the terrain we hunted, 90% of our shotgun kills were 40 yards and less.
With kids and Dad shooting, somehow, you have to get the cost of shells down. Also, the availability of components, compromises have to be made. There is usually one guy in the family that is loading for brothers, uncles, nephews, and his own children.
Lee makes a great #4,00, and 000 buckshot mold, and going down this road is like a hobby within a hobby with load and choke testing....keeps the family shooting.
Great close range (40 yd and under)coyote shells can be assembled with simple hulls and wads unless you are wanting long range shells were the TSS shot will really shine.
A simple Mec Jr or Size master is all you need to get started on loading your own buckshot.
It is prudent to get into loading your own, buy what components you can afford for a 5 year period.
If a guy had the means, it would be smart to buy up about 10 lbs of TSS shot, and 20 lbs of Ballistic's products products buckshot in the sizes you like, #4, F, and T shot. You would be set for life for all the types of terrains you would be hunting in.
The main issue, is to get into reloading your own buckshot, patterning your shotgun with different chokes.
I have skinned a LOT of coyotes, 3-4 #4 buck in the chest puts a coyote down, and 8 T shot would probably be better. My rule, if they are twitching a tail, hit them again!