Hanging string lights from stone
I would only drill that stone as an absolute last resort. That not only damages it in an unrecoverable way but opens it up to faster degradation from weather, especially if you're in a frost zone. 

Get some aluminum wire for bonsai (example). It's anodized in a suitable color and very easy to work with. You could also use coated steel gardening wire (per Tonny's comment) or even coated copper electrical wire. Wrap it around the stone and twist it at the light location, then use the tails to attach the lighting. As Criggie suggests in a comment, you could use a wiring strategy similar to how sparkling wine bottle caps are done:



You could also use decorative metal strapping (examples). Wrap it around the post, folding at corners, and use a bolt to cinch it on the outside corner. If you leave a gap between the straps you could attach S-hooks or similar to the bolt shank.

Whatever route you choose, protect the wire well from chafing to prevent damage and shorts. (Thanks, Chloe.)