Draw a square on the ball, centered around the puncture spot.
Use a craft knife to cut the ball cover on three sides on the drawn square. Cut the foam that is underneath the cover, but be careful not to puncture the bladder of the ball.
Apply a thin coat of rubber cement to the puncture on the bladder of the ball. Do not proceed until it is dry.
Press the bicycle tire repair patch over the puncture, on top of the rubber cement.
Spread glue over the bicycle tire repair patch and press the cover of the ball back down over it.
Wrap duct tape tightly around the ball over the area that was punctured. Leave it wrapped overnight. When you unwrap it the following day, pump the ball up with the bicycle pump.