Get a piece of PVC (vinyl) liner patch material that would provide a surface approx 2" larger than the slit all the way around the slit.
If possible, rough up with sandpaper both the area around the slit and the patch, then wipe away any dirt or grit.
After roughing with sandpaper, clean the patch with alcohol (rubbing) or acetone.
Following all directions and precautions on the package, mix up enough glue to cover the patch, then stir it every few minutes until it begins to thicken. The amount of time required to do this will vary depending on the temperature. Higher temperatures will cause the glue to cure more quickly. At 70 degrees Farenheit, the glue will cure in 30-60 minutes. By stirring the glue until it begins to thicken, you will minimize the chance that the water will penetrate the patch before the glue sets.
Apply the glue to the patch. Then simply put the patch over the liner slit pressing lightly. Be sure to leave some glue in the bond area, don't press so tightly that all the glue is pressed out. Hold the patch in place until the glue hardens. If it is a vertical patch it is possible that it could slide down somewhat until the glue hardens. Smooth and taper the excess glue out around the patch for maximum strength.
Let the patch cure overnight before putting stress on it.
Clean any uncured glue off of your hands etc. with rubbing alcohol.
Swim! If you apply the glue correctly, its bond will be stronger than the pool liner.
