A few years ago I did some articles on cutting CD's and using CD movement trays. This all goes back to the playtesting of Ganesha's Harder Than Steel, that required same.
Type 1. I put a rough bit of card over the holes then covered each side with generic no-more-nails. Painted up in different scheme. Problem is, my green mat, they stick like velcro. Now consider these are years old- rough storage and handling, no chipping, no side of wear.
Type 2. Made as above but a very thin layer created as the rings for my Olympics project. Surprisingly robust! Even the chalk I rubbed over them is still there!
Type 3. A copy-ish of modern laser cut. A piece of cereal packaging card, holes cut out (oh what fun!), cut out then added to a thin layer of guess what. A bit more gunk added. I'll flock this eventually, just like a figure base.
Type 4. I did these yesterday for use today in comparison with type 3. Watch this space! A number of pennies on card, pencil around then cut out- add to CD. I added the cut-out form to the base to raise up & make it easier to lift. Now I need to see how they photograph in use.
BTW, you leave overnight before cutting!