Place on a cutting mat a piece of rice paper in a color that matches your divider or that contrasts with it. For example, you can place a blue heart or a red kite on a tear. In this way the match serves both a useful and a decorative purpose.
Place a stencil on top of the rice paper. For example, you might select a flower shape, a heart shape or a circle shape for your patch.
Trace the stencil with a razor craft knife -- making sure not to cut anywhere near your fingers. Do not trace the stencil first with a pencil, as rice paper is translucent and will show on the room divider. Trace the stencil a second time on a new sheet of rice paper so that you have two identical patches.
Apply acid-free craft glue around the edges of the patch. Place the patch over the hole in the room divider on each side of the divider. Allow the glue to dry.