Bookbinders tape AKA library tape.
If you try gaffers tape, make sure it's Gaffers tape NOT duct tape or some other sorry excuse. The adhesive will become gooey over time.
You can also use black silk binding tape available from Freestyle. That is working fine for me. Clean the surfaces of the holder before applying the tape. After applying the tape trim it to fit the recesses in the holder with a razor blade. I cleaned the holder surfaces with MEK but it took off paint as well. I repainted the holder with some flat black before taping.
I used gaffer's tape to repair a couple of 4x5 wooden holders. It worked great and I have lots of gaffer's tape left over if I have to do more. Black duct tape would probably work just as well. No need to get crazy with exotic stuff for this job. Really.