The easiest fastest cheapest thing would be to beef up the existing door by trimming it out with 1x6 or wider pieces of Actual Real Lumber all around the edges and possibly a couple across the middle too. Important: clamp or temporarily-screw the plywood down to something flat (like, F-L-A-T really truly dead flat, not jsut sorta) while you do this. Screw 'em on in many places. *Hopefully* you can get the warp out of it sufficiently well that way.
Then prime and paint it; helps vs warping as well as durability.
Or, build a door out of 1xwhatevers (ideally tongue and groove) with a Z of battens across it to hold 'em together. The slanty batten that goes diagonally across the whole door has to to from the lower hinge corner to the upper free corner, not the other way 'round. This will be a bit heavier than your plywood door (translation: need bigger stronger hinges, bigger stronger longer screws, and a bigger stronger post to screw the hinges onto) but it will warp less and generally be stronger and more durable.
Or you could find a salvage door (EXTERIOR, not a hollow-core interior door!) and retrofit your coop for it.
Good luck,
Pat