well there's carpenters glue. it keeps it's dimensions after drying (doesn't shrink and leave gaps).
i've used Gorilla glue a bit recently. It also seems to keep dimension but surfaces need to be wet to 'activate' it.
http://www.gorillaglue.com/home.htm
edit: get some kind of syringe to inject it where you need it -- just some disposable ones since it's gonna be a one shot deal anyway using glue!