How do I restore flat couch cushions that don't detach?

There should be little narrow part that hangs over. Under that, make a small incision. Add stuffing, you can get this at any Joann's Store. Sew it back up, or to be extra creative, sew in a zipper so you can restuff as needed.

Answer

Chances are that the original stuffing is a foam pad. If you can remove it through the incision, take it to the fabric or upholstery store (camping stores also have foam) and buy foam of a similar size and thickness. You may opt to upgrade the foam to a more dense version so that it holds its shape better.