Federal makes a #4 premium buckshot load which I would consider for coyotes out to fifty yards.
Premium Buckshot
Our Buckshot delivers staggering ballistic capability. Our patented spiral shot stacking process, with plastic shot cup and buffering, ensures dense, predictable patterns. Copper-plated shot penetrates deep for harder hits.
34 PELLETS - 4 BUCK
P156
12
2.75
MAG.
1250
I believe that at one time Remington also sold a magnum #4 Buck load that was nickle coated.
At one time I did a bunch of testing at different ranges in light brush cover and in the open using 2 3/4 length #4 and 00 buckshot loads at taxpayer expense. My conclusion that buckshot was good out to about 30 yards in the open. To be effective with buck you need to have a number of hits on a target. After 30 yards the pattern was to open to insure enough hits. I would backup my buckshot with rifle slugs.
Suggest cutting out a coyote silhouette and create a backing of four or five layers of heavy card board or a thin piece of plywood and see what kind of penetration you will get and coverage. You will need at least three pellets in the heart/lung area for a kill. Back in the days of lead shot I killed a lot of ducks and geese with #4 lead shot. It was very effective on a five pound duck or a ten pound goose but I do not recall full pentration of a bird with #4 shot.
I tried penetration shots using #2 lead bird shot on 1/4 plywood and I feel it would be effective at 30-yards in a magnum load. dougk suggestion of 3-inch BB or BBB maybe just right.