Locate the leak. If you see the leak, skip to Step 4.
Get the hand pump that is used to fill your stability ball. Remove the plug on the stability ball and insert the head of the pump into the stability ball. Pump the stability ball until it is full of air. Put the plug back in.
Pour water over the stability ball and give it a continuous gentle squeeze. You should see the water start to spray away from where the hole is located. If it is not immediately apparent, pour the water on a different side and rotate the stability ball until you find the hole.
Use a marker to make a small mark on the spot where the air is leaking. This will prevent you from having to find it again if you lose track of the spot.
Buy Goop adhesive. Sports & Outdoor Goop or All-Purpose Goop will be best for patching up a stability ball. Goop is sold at most home improvement stores such as Home Depot and Lowe's, and a small tube can usually be purchased for about $5.
Cut out a patch of duct tape to roughly form a square. Cover this patch of duct tape with a thin layer of Goop.
Fully inflate the stability ball.
Place the patch of duct tape face down on the stability ball where the hole is located. Smooth the duct tape out with your fingers and remove the excess Goop that comes out from the sides. Acetone and naphtha are the best chemicals to use to remove the excess Goop before it dries. You can still remove the excess Goop after it dries by simply scraping it, but be very careful not to make another hole.
Wait a full 72 hours before trying to use the stability ball again. It may not take that long to dry depending on the humidity and heat, but it never hurts to be on the safe side.