Oddly enough I have drilled stone on a drill press, marble though which is pretty soft and easily drilled. I’m kind of guessing you’re working with something harder though, otherwise you would be using a hammer drill. The only other options that come to mind are verging into the realm of coring bits with are essentially annular cutters but with diamond tips. They have the capacity to drill (“core”, more precisely) to the depths you’re looking to achieve and could probably be driven by a decent drill press press although the speeds might be too fast. I’d do it wet using water as a flood coolant.
There are small diameter diamond coated bits made for putting holes through ceramic tile (think shower faucets here) but the tend to be a bit short. Maybe you could weld or braze on a shaft extension to get more depth, I don’t know. You’d need to play with one. The nice thing about them is the diamond particles are adhered to the outside of the cutter tube, so there would a clearance created to the cut and should allow for depth provided you could extend the driving shaft. Hmm, depth is limited by the back of the cutter, darn, you’d need to try to snap layers off as you go deeper if that’s possible. Coring hits solve the problem by being long tubes already.
What stone material are you fooling with, and what’s the purpose for the holes?
-frank
