Have you looked into ultrasonic drilling? This uses sound waves to drill a hole or even sculpt out entire pieces from precious and semi-precious stones. It's a widely used method here in Japan from drilling precious and semi precious stones. Most of the equipment is either USA or German made.
In Germany this technique is widely used for drilling stones and fabricating sculpted gem stones. In the USA it is more widely used for fabricating electronic and nao technology components.
Of course, depending on the Mohs rating of hardness of the stones you are using, there are many other options including even HSS (High Speed Steel) . Diamond drills are readily available, and very good quality, relatively inexpensive sintered drills are made in the USA. Also, if used with care ordinary HSS drills can drill some stones.
Finally, there is the time tested method of using an abrasive, a copper tube and drilling under water.It's a subject with almost no end of variations. I've done a lot of glass drilling for clocks I've made, and this is generally a much more difficult material to work with than most gen stones.