Materials That Hurt Coins

I would think cork, being an oak product, would be very acidic in it's chemistry. That being said I would think it would be bad for coins

Get a sheet of clear acrylic from the hardware store. Acrylic has no'PVC in it, is clear, and would show off the coins well. Only downside it it can be a bit pricey

Depending on just how permanent you want to make that display, one possibility is to make the entire thing in plastic. For example:

I made this in 1959 and it still looks the same except for some nicks from me being careless.
You could lay out a piece of plastic in a frame, layout the coins you want to display, pour liquid plastic over the entire layout. Naturally you would have to seal the edges on the bottom during this process so as to now allow the liquid plastic to leak out. Simple tapiing would work.
Liquid plastics are available in many hobby type stores and similar places.
The worst part of this is those coins are now there forever. The good part is they will never corrode, rust, tarnish, stain, tone, etc. What you see before is what you see in a hundred years. The moral of this is to use only coins you don't need, want, can use in an Album.
Not to long ago someone posted a photo of coins in plastic in the shape of a toilet seat. Actually looked good enough to hang on a wall.