The BEST CA Glue I know of is "PROFESSIONAL" Locktite brand in a blue bottle. NOT Thread-locker, but CA Glue. It is sold in Home Depot and is about the ONLY CA glue I know of that truly works. It has the "professional" rating on the label I suppose to signify it is an upgrade from the run of the mill super and crazy glues that only really seem to work on fingers.

Carpenters Glue would work well but in getting enough between the crack might cause it to split even more since it is quite a bit thicker. I suppose you could thin it out a bit to apply it with a needle though.