I have started clearing out a rectangular space to store the pegs and then a using a dovetail bit and coming in from the edge to carve a space for the cover to slide into. I then carve covers using the same bit so I get a cover that slides into the slot. Both parts get a small circle to glue a magnet into each part to keep the cover from sliding out. I am replying on my phone so I can’t share files but I can probably try tomorrow. I also like @WillAdams idea of the rectangular hole with a circle inset around the outside.
Here is a link to an example I did with a euchre score board.