Instead of recaning a missing seat, we made a wooden one and topped it with a matching cushion made by an upholsterer. The frame is painted a burnt gold here. For a truly coordinated look, have a seamstress create a Roman shade and duvet cover, too.
1. Tape kraft paper over the open seat, trace the groove around the inner rim and cut it out. Cut that shape out of 1/2-inch-thick plywood and sand edges. Cut the shape again from 1/2-inch-thick foam. Cut out two more layers, one from batting and one from fabric 2 inches wider all around than the others. Lay cloth face-down; stack batting and then foam and wood on top.
2. Fold edges of batting and fabric over wood; fasten with a staple gun. Attach piping with staples. Secure seat to chair using screws and mending plates.