Most vinyl liner swimming pools at some point will develop a leak. Whether it is from something sharp poking its way through from underneath the liner or something like a toy or more commonly, a vac pole without a vac head or brush on it is used to retrieve an item from the pool bottom. It will happen. Once you find the hole, now you have to patch it. This can be done underwater.
There is no need to drain the pool. (please read “don’t drain a vinyl liner pool” under “pools”) Swimming pool glue is made to be used underwater. The most popular brand of underwater glue for patching pool liners is made by the boxer. If you shop at a “big box” pool store the patch kit you are going to find is either going to be a self-adhering patch that you peel and stick a thin piece of plastic over the hole, or a slightly thicker piece of clear vinyl that comes with underwater glue that you cut, apply glue, and stick on.
Both of these options will probably work short term. If you are looking for a permanent fix, head to your local pool store and ask them how they would patch a hole in a vinyl liner swimming pool. You will get the same response you would get in my store. Use a piece of a pool liner and underwater glue and make your own patch.
This way you are making a patch that is the same material as your liner. I would go to my box of liner samples from previous years, find the closest match to your liner pattern, cut you a few pieces, get you a can of glue, and tell you how to do it yourself when cutting the patches, always make the patches round or round the corners. this will keep the edges from peeling up. To patch a hole on the bottom of a swimming pool, hold the patch in your hand, apply a generous amount of glue to the patch, fold it like a taco, dive down holding the patch upside down(so the glue doesn’t float out) and press it to the hole. Use your fingers to seat the patch properly by pressing down and making sure it is attached across the whole surface to the liner.
This type of repair should last as long as the liner does. You will be able to vacuum and brush your pool without fear of the patch coming off.