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Qualceram Shires Linear Pan Cistern & Fittings Seat & Cover
If the piece you remove is too badly damaged you may have to cut a small piece of drywall to fit. The problem here is that drywall comes in 4-by-8-foot pieces. Don't buy an entire piece.
Drywall gets damaged regularly at home centers and lumberyards. Check to see if they have a damaged piece they will sell you at a reduced price. Or better yet, ask if they will give you a small piece salvaged from a severely damaged sheet. We've even been known to Dumpster dive at construction sites.
Once you have a hole in the wall, cut a piece of wood so that it is a little wider but not as long as your 6-inch-square opening. An 8-inch by 5-inch piece of scrap ½-inch plywood will do.
Drill a small hole in the center of the wood and thread a string through it.
Knot the string or tie a nail or metal washer to it so that the string can't be pulled out. Make sure you can work the wood through the hole in the wall and that it can be pulled up against the back side of the wall by the string.
Once this backing is prepared, apply construction adhesive around the edges of the plywood and, using the string, pull it securely against the back of the wall. If there's enough room to get a finger or two behind the plywood, you won't need the string.
While holding the backing in place, drill a couple of pilot holes through the wallboard and into the plywood. Then secure with 1-inch drywall screws, making sure they are countersunk.
Let the construction adhesive dry - 24 hours to be safe - and glue the piece of drywall you removed and saved to the plywood backing.
Tape the joints with drywall tape and finish the patch with joint compound. It will take at least three coats of joint compound to properly finish the job.