3M makes a great spray adhesive called Spray 90. Or maybe Super90 now. You can find it at Lowes and Home Depot. They also sell Spray77 and it is NOT the same strength. Get the Spray 90. The fumes are fun...I mean use a respirator with it. Spray both surfaces with a medium to heavy coat, let it tack up and then stick it. It will still stick even after both surfaces dry to the touch, just stick it when you are ready. But be warned, when it is stuck it is STUCK. Get it right the first time. One can goes a long way. It also has an adjustable fan and volume control nozzle.
You can get vinyl at just about any fabric store and that 3M product works great with it.
EDIT: The gorilla glue is good for a lot of things but it can get brittle and let go at the corners or edges. The 3M Spray 90 is much better for this kind of thing. There are other types of spray adhesives from industrial sources but they are just stronger versions of the same thing.(Spray 90)