Titebond. Wayne Henderson in VA builds some of the very best acoustics; he's built over 350, including two for Eric Clapton, and he's used Titebond for every glue joint on every one of them.
I just glued a poplar dowel into a piece of purpleheart with this, and now it's all "AS ONE" - safe for drilling, routing and such without fear of shattering or fragmentation.
How do I know?
I drilled it. It machines just like wood. Highly recommended.