Plain old super glue, fast, safe easy. For stronger bonds combine it with baking soda. Add a little super glue on one piece and press the other piece into some baking soda and join them. They will never come apart again.
Non aquarium silicone is a iffy bet and it takes a few days to cure and it's messy and unsightly. Superglue is inconspicuous and if you're careful it can look good.
There is no cure time for super glue. After a light rinse in water you're good to go. If you're using a lot though I'd suggest an over night soaking. Water makes super glue harden and cure faster.