Here’s my thread regarding using PCD (poly-crystalline diamond) bits to carve marble tiles for coasters. I feel like I am spamming this link, but I haven’t seen any other posts regarding carving stone (vs engraving stone), so here it is again. 
I bought diamond bits from AliExpress. They took 3ish weeks to arrive, but were ~$12.00USD each vs ~$175.00USD for the Amana bits from sites like ToolsToday.com.
Good luck and please report back with pics and any additional info you can think of. Things that worked well are nice to hear. Things that went bad are even better to hear about so the next person doesn’t make that mistake as well.