Go to a foam and fabric supply store, one that sells upholstery supplies. Get a can of HH66 vinyl cement. You can likely buy a scrap piece of vinyl fabric in the same store. The cement works great when you follow the instructions, especially if you heat up the vinyl before applying and use a rolling pin to roll it out flat where the patch overlaps the fabric that needs repair. Let it dry over night and good as new.
There is also a very handy product call Tear-Aid that comes in strips of about 3"-12" long that has adhesive on it and a peel off backing. This works great in an emergency to do a field repair. If you cant find this at the fabric store, look it up online.
I used to be the Operations Manager for Party Outfitters, the interactive game company that provides inflatable slides, bounce houses, and other inflatable vinyl games and rides. For us, being able to do field repairs was a must and the Tear-Aid was provided to our staff on every event. The HH66 is the stuff we used for permanent repairs in the shop.
Hope that helps.
The cast that catches the fish is never too short. Patrick McManus