I either saw one of these at the store or online, actually built one for launching oranges a couple years ago.
For water balloons, get some sort of strong material as the
basket, I would recommend you cut a
PVC pipe down the middle. Cut two holes in either end of the
PVC pipe, and run a piece of surgical tubing (1/2" diameter is plenty) through either end.
For handles, get a couple pieces of threaded rod (along with eight nuts to fit), perhaps 12" long each, and
bend them to make handles. Put one
nut on the each end of the handles and thread them up a ways. Slide the handles into the holes on the back of the pipe, and using the remaining nuts to lock the handles in place. You may want to get some of the plastic tool dip at Ace and dip or paint the threaded rod in that to avoid scraping up your hands.
I used a 8"
PVC pipe cap when I built mine, but it was for launching single oranges. Be careful with one of these devices, we had an accident with an orange that didn't leave the launcher and backfired.
I can get some pictues of the orange launcher if you need them.