Reddit mentions of Foam Ring Pad Half Size Black Tray Inserts Jewelry Display

I would try to find a wholesaler that sells gift boxes to jewelers, and see if you can find a ring gift box with an insert that fits your box.

Here is the kind of thing I would look for.

ttps://www.jewelrydisplay.com/jewelry-gift-boxes/ring-boxes

If you are in a reasonably large urban area there may be a local wholesaler who could give you a better idea of what is available.

Another option would be to buy a Foam Ring Pad Tray Inserts Jewelry Display that is the right dimension so that you could cut off a section to fit in your box.)