I'm Adam, and about a week ago I created my first pneumatic cannon using 3/4" PVC for both the chamber and the barrel, as well as a 3/4" sprinkler valve. This was to test out my construction techniques, and give me some experience with a small cannon before moving on to bigger things
It lasted about a day before the barrel and chamber were both upgraded to 4 feet of 2" PVC.

I have previous experience with water rockets (my personal record is 460') so migrating to cannons wasn't too huge a step for me.
I now have two goals:
1. Make the cannon more compact (the current configuration is about 9 feet long)
2. Make the cannon more efficient/powerful without making it bigger
I discovered the wonderful world of Spudfiles a few days ago, and have been reading as much as I could since then. When I stumbled upon piston valves, I knew this was what I needed.
I designed it in paint, and I think that it should work, but I want to run it by the experts before I actually make it.
I plan on the piston being a duct tape wrapped caulking tube filled with hot glue, and the seal being attached with a nylon bolt and super glue. The bumper will be made out of some foam insulation.
By some miracle, my local Home Depot has all the materials in stock, at least when I check online. I did not expect them to have half of what I needed, but perhaps it was meant to be.

I based my design on Mr. Crowley's instructable, many thanks to him and all who answer.
Thanks again for the help! 8)
-Adam