Anything between BB and #4 is great. The larger shot sizes aren't ideal as they start to pattern pretty sparsely at over 40 yards, and a coyote is a small target. On the flipside, pellets smaller than BB don't retain enough energy to penetrate well at distance.
Within that general shot size range though, I'd suggest you experiment and see what patterns best in your gun/choke combo, and go from there. My best success has been with Remington's 12ga 3" buffered 41 pellet #4 buck load through a full choke in my SX3- it'll put an average of 10-12 pellets on a pie plate at 50 yards, which is plenty dense enough with big pellets to kill a coyote.
I'd avoid any steel shot, as it loses velocity and penetration very quickly at distance- lead or lead-alternatives are far superior, and worth the cost for coyote hunting.