Epoxy, also for finishing off mix loads of the stone dust (from drilling) with clear epoxy as a filler. You need to brush the stone thoroughly to get rid of any loose stuff, you can't glue dust to dust. If you can peg it all the better, or even drill some small holes to give something for the epoxy to grip into, any increase in surface area helps to make it stronger.
Make sure you have enough epoxy to hand, mix it very thoroughly, you only have one shot, figure out how you are going to hold it together first.
I'd be tempted to use standard epoxy, takes a longer time to set but if things start going wrong fast-epoxy limits your recovery chances.
Gripfill, stixall, hippo etc may well work but epoxy has got a long track record, its even used to hold rock walls together (together with pins).