What kind of finish do the panels have? An option is wood filler. There are wood fillers out there that you could use, but first, you must install a piece of wood backer with glue.
Then the wood fillers... ELMER's has some in wood colors and some to be stained. May be one of the colors may work or you may have to tain. You could get get a couple of colors and test-dry a sample. You will have to apply in a few coats of filler using an artist's spatula to shape it in, in particular for the last coat. Once dry they can be sanded or scraped with something sharp. If you have a bit of craftsman/artist hands, it could be sealed and paint a couple of very dark rings with a fine brush, then dab dark stain over... It will always look as an irregularity, probably the darker the better.