You will either need an air mattress repair kit or the equivalent components: an adhesive and a piece of vinyl that’s larger than the hole you’re repairing.  Use any vinyl repair kit instead of an air mattress repair kit.  Choose an adhesive that’s made expressly for sealing seams. Try McNett’s Seam Grip or Coleman’s Seam Sealer. You can also consider using rubber cement. Duct tape can be used in place of the vinyl if no other alternatives are available.  You may also need something with which to apply the adhesive. A small paint brush is ideal.  Use the applicator that came with the adhesive or small paint brush. Make sure you cover the entire surface of the patch. If the leak is small and in an area where a patch cannot make full contact with the mattress fabric, you can try plugging the leak with a small a bit of adhesive. Press firmly and smooth it out. The goal is get the patch to make full contact with the mattress. Consider weighting down the patch with a 10-pound weight to ensure full contact between the patch and the mattress. Exact drying times will depend on which adhesive you’ve used. Refer to the directions on the package.
Gather your materials. Measure and cut a patch that’s at least ½ inch bigger on all sides than the tear. Apply the adhesive to one side of the patch. Press the patch, adhesive-side down, onto the tear or hole. Let dry for several hours.