If the mattress is new, a leak in the seam may indicate a defect or poor quality. You will need an air mattress repair kit or the equivalent components: a vinyl adhesive and a vinyl patch.  When purchasing adhesives, look for urethane glues like McNett’s Seam Grip or Coleman’s Seam Sealer. Instead of urethane glue, you can try rubber cement.  Use the applicator that came with your adhesive or a small paint brush.  Make sure the adhesive extends ¼ of an inch beyond the edges of the tear. If you’re fixing a seam on a flocked surface, use more adhesive to ensure that the two sides of the seam stick together. The goal is to make sure that both sides of the opening remain in contact while the adhesives sets up. Consider using clothespins to hold the two sides of the tear together. Just be careful not to glue the clothespins to the mattress. This is called “setting up” and will take a few hours.   Drying times will vary depending on the adhesive but 6-8 hours is a good bet.
Consider returning the mattress. Gather your materials. Cut a patch from a repair kit or a spare piece of vinyl so that it will cover the tear. Smear an ample amount of adhesive over the tear. Press the two sides of the seam together. Let the adhesive dry almost completely. Apply a layer of adhesive to the patch. Place the vinyl patch onto the newly applied rubber cement, following the instructions on your repair kit. Allow the adhesive to dry completely.