That depends on what type of stone. Hopefully they are something soft like marble.
Stone can be drilled with a star drill, which is a cruciform cold chisel that you smack, rotate, 45 degrees and smack again, clearing the chips from the hole as you go and it takes forever. There is no doubt an equivalent pneumatic hammer drill bit that works much the same way. But 1/16" would be pretty delicate.
Another older and much slower way is to use a drill rod, usually of a softish metal or even (on-topic) wood and an abrasive slurry. That is probably how the ancients did that sort of thing before they had metals hard enough to make star drills. Sounds like a job to assign to an apprentice or a slave.
A laser might be helpful, but probably not available to you. Professional shops that work with granite counter might be able to do it, or know how.
If they are 'lucky stones' (e.g. quartz) I think you're out of luck.
You need diamond drills and you need to use a drill press with the stones in water (water covering the drilled area). If you never done this you must go slow and expect to break some drills.
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