Another way to drill stone is with a tube drill and loose grit. I don't think it's a good idea to drill stone scales, though; it'll end up weaker than if you just used epoxy without rivets or pins. Make deep gouges in the agate with a dremel, clean the heck out of both surfaces with solvent, and glue it up with JB Weld -- and don't clamp it too tight.
If you're totally paranoid about any possibility of the scales coming off blind pins would weaken the scales less. Or you could inlay the agate in metal; that would be the strongest way.
I'd worry more about the agate breaking than the epoxy failing, though. If an epoxy joint is done properly it's much stronger than agate. Cleanliness is vital to epoxy; most people don't clean the surfaces enough. I also like to heat-cure epoxy to make sure it hardens fully -- it doesn't need much heat; putting it near a light bulb will do it. You want it warm to the touch but not hot enough to burn you for a couple of hours after it appears to be fully hardened.
-Cougar Allen :{)