It occurs to me that people looking to polish stone counter tops may also be looking to make holes in them. May I suggest looking to Harbor Freight for diamond hole saws. Elsewhere they are $50 to $200 each. I needed 36 holes, 3/4" in diameter, in 1 to 2 inch thick slate (I think the largest they have is 1 or 1-1/4 inch). After being put off by the high prices from "regular" suppliers, I purchased the diamond hole saw kit from Harbor Freight. Being afraid one hole saw wouldn't last (only one of the correct size was in the set), I purchased two more sets -- I think they were $15 for a three hole saw set. I also bought a small drill press from them for $39 with the express intention of ruining it with water spray while I drilled these holes. The saw wasn't deep enough to punch completely through, so I had to purchase an extension (and cut it shorter to fit in the drill press). Then I had to drill until the core filled the saw, pop the core out and continue until the hole was punched through. (Be sure to use running water to cool the work and remove the waste stone sludge.)
bottom line -- I drilled all 36 holes with only *ONE* of the diamond hole saws from Harbor Freight -- and I actually drilled over double that number if you consider that I was drilling to a depth much greater than the depth of the saw.