I'm not a chemist, but I have a lot of gluing experience. 3M makes a very aggressive glue for polyethylene which will glue just about anything, and has some gap-filling ability. It's a 2 part, static mixed type. I think the designation is DP8005...but I can't remember for sure. If your application is not too demanding I'd also try silicone glue.
Seems like an epoxy would be a good candidate, particularly if you can scuff the bonding surfaces. The Loctite company would be another good place to check with, http://www.loctite.com
Hi Peter - I agree regarding Loctite, but would also suggest you try one of the better hot-melt adhesives, or a water resistant pressure sensitive tape - some medical dressings are made from this.
