The little wood filler sticks available at Home Depot or any other similar store will work just fine. They are designed to fill nail holes on wood trim. You can choose from a variety of shades and colors to closely match the surface you are filling. Another option, if you can identify the wood where the holes are is to find a scrap piece of matching wood, grind up some sawdust, mix it with epoxy and fill the holes. Once dry, just sand flush and rub on some compatible finish. Good luck.
--Mike Dunnaway