Inside view of Emery's idea

Simply use the panel that is under the couch and set it in the straps. It looks comfortable and doesn't require any string/rope or wire. It also already there and you don't have to carry anything extra. You probably could also set it in upside down with the padded section closest to the bunk. BTW if you want to make the bed more comfortable for the kids try taking a full size comforter and folding it in 1/3rds. Then use that as a mattress. That way the bed will be more comfortable and the kids won't be uncomfortable with the buttons in the upholstery. They'll sleep better.