Forgive me if this is the way everyone has always done it, but this idea finally occurred to me yesterday so I thought I should share it. I'd been trying my best to find the exact center of epoxy-filled holes so the drill for the final hole wouldn't hit bare wood. My best option so far has been a circle template with four tick marks that I used to draw diameter lines at right angles. But I still usually got it a little off--it's not as easy as it sounds.
The solution is a Forstner bit. Use the one you used to drill the original (larger, filled) hole. Or if you used a twist bit to drill the original hole, find or purchase a Forstner bit of the same size (they are worth it). The Forstner bits have a little sharp point in the exact center used to start the drill. The bit should not be mounted in a drill chuck. Place the bit over your filled hole and carefully align its edges with the rim of the hole. When you have it perfectly aligned, just press down on the bit and twist it a little to make an indentation at the center, being careful not to scratch your work at the edges with the drill's cutting surfaces. That is, try to keep the drill bit perfectly perpendicular to the work, and don't press down too hard or too far. If the indentation at the center needs to be a little larger, take care of that with an awl or a prick punch.
Again, I hope I'm not telling you something you already know, and that this will be helpful.