Add an outdoor sealant to the wood. Painting or sealing furniture for outdoor use is different from painting something for use indoors. If you want to move furniture that was made for indoor and outdoor storage, you'll have to completely seal it with an outdoor sealer. To waterproof a dining table, sand the surface until it's smooth and remove all the old paint.
Then seal it with a coat of outdoor wood paint and at least 3 coats of sealant, such as polyurethane, until it is as smooth as you want.