If I were to approach this my first thoughts are that I need some backing support. First I would clean up the hole with an x-acto knife or whatever. Maybe even consider cutting the hole so that it is square. I would then play around with some materials that could serve as a backplate (balsa sheeting for instance). The back plate needs to go "into" the hole and attach (with glue) to the rear face of the coverite (or balsa if there is balsa under the coverite). What you are trying to do is build up a surface to attach to. Use this sheetrock video as an example. Especially note the wood backing at the 6:24 minute mark