Strong adhesive such as super glue gorilla glue contact cement or rubber cement.
Silicone glue for air mattress.
Next cut out a square of thin plastic big enough to extend a centimeter past the hole on every side from something like a shower curtain or tarp.
Now patch the air mattress hole with this sticky piece of plastic and press down firmly rubbing in a.
To patch a leak in an air mattress start by using sandpaper to lightly scrub away the soft felt on the surface of the mattress around the hole to help the glue stick better.
Pvc stitch liquid patch glue is 1 solution to permanently fix rips seal leaks on pvc and vinyl inflatables boats swimming pools air mattresses waders neoprene wetsuits polyester tents cords and other gear.
In a pinch use squares cut out of a t shirt applying gorilla glue both to the surface area of the leak and to the cloth square before adhering them together.
Be careful when applying the hot glue not to let the tip of the glue gun make contact.