I've used duct tape, and it works well on waterbed matterss material as well, which is thicker and stronger. Bit messy though.
There is a right glue for everything, so says my Ma who worked in that field for years. However for small vinyl hard parts, nothing seems to work. I would suggest looking into a heat sealer. It seems to me that just about everything made out of such material is "sewed" that way.
[url=http://www.hobbylinc.com/htm/amb/amb1611.htm]This should do you nicely, but make sure you're in a well-ventilated area, with eye and respiratory protection.