Well, that's a loaded question that will only be solved by range time and a patterning board.
In theory the tighter the choke the denser the pattern at longer ranges. In reality once you get above a certain shot size you get diminishing returns and can actually get some blown patterns from deformed over-choked pellets.
Most people seem to use the larger birdshot sizes or smaller buckshot sizes for coyotes. There are also dedicated coyote loads out there today, but I'm not sure that any are available in 2 3/4". If not, I'd start with some "T" size non-steel shot (hevi-shot maybe?)or #4 buckshot with a choke of appropriate constriction and go from there.
Carlson's makes a "dead coyote" choke tube that you may want to try. I've read good reports on it but never used one myself. All of my coyote shotgunning has been done while deer driving and the yote's were trying to sneak through. In those cases I was using 00 and a mod choke but the range was only about 35-40 yds max.
You'll need to pattern test your gun/choke/load combination at the ranges you expect to shoot though.
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