If you use glue use epoxy. If you use epoxy I like the instant install for this application as it is knife grade and fast setting.
I do have a concern that the breakage of the bottom of the stone may have weakened other parts of the stone. Or am I misreading what broke?
If any of the stone was broken I would expect other parts of the stone near the break to be weakened. can you use undermount supports? They are tied into the cabinet so the gravity works with them and not against them.
here is a link for the Instant Install epoxy:
http://www.defusco.com/Glues:-Epoxy,-Polyester,-etc.-Epoxy-for-Natural-Stone/c82_500/p2423/INSTANT-INSTALL-29-MINUTE-EPOXY---32oz-KNIFE-GRADE/product_info.htmlHere is a link for the undermount sink brackets (2 brackets comes in the kit, one for either side of the sink):
http://www.defusco.com/Prep-Tools-Undermount-Sink-Bracket-Kit/c89_714/index.htmlGlad to be of service,
Mark