what is the best way for me to fill in old sight holes?
With an old sight.
Sorry, but that was too easy!
Bowdoc has better advice, and I remember he likes to use a wood plug to fit most of the hole, and then top it with epoxy. He says that you must be careful about just using epoxy, because in time it will shrink.
i use a matchstick and epoxy...
put epoxy into the holes and on the matchstick as well, then leave the nubb of the matchstick 'high', wipe clean with a damp cloth, to very lightly sand down to match the surface, stain/paint.
match sticks are softer than the traditional wood dowels and easer to sand down is why i choose them...
do the drill (practice) on a piece of scrap wood first though to get the idea of how much to apply. it takes very little
you could go ahead and drill them out and put in bushings.
Any kind of epoxy work or do I need something special? I have a two part epoxy that I used to glue a side mirror on my car back together.
Any epoxy should work. If the holes are in glass, not wood, add some color to the epoxy to match the color of the glass. Overfill the hole and sand & buff to smooth it out.
I learned this from a guy that refinishes old bows and it works well for sight and quiver mount holes in the wood.
Clean out the hole with a drill bit. Use a bit that is just a little bigger than the piece of dowel rod that you want to use to fill the hole. Cut the dowel rod just a little shorter than the actual depth of the hole to be filled. Find a magic marker that best matches the color surrounding the hole to be filled. Lightly color the outside facing end of the dowel rod with the marker. Try to keep the end of the dowel rod a little lighter in color because the final step will darken it a little more. Use sparingly some wood glue on the dowel rod and insert it in the hole. The goal is to have a very shallow well when the dowel rod is fully seated. Let it dry fully. Once it is dry use a 5 minute two part clear epoxy to fill in the well. The epoxy seems to match most old recurve finishes. Once the epoxy hardens fully, sand it smooth. If there is still a small well, add some more epoxy and wait for it to cure. If the rest of the finish is glossy, polish the sanded area to match.