Mix your own solution to remove the stains from your antique porcelain. In a small cup or bowl mix a quarter cup of cream of tartar, and a tablespoon or two of hydrogen peroxide to form a thick paste. Alternatively, you can mix a 1/4 cup of borax and enough fresh lemon juice to form a thick paste.
Use an acidic cleaner instead of the homemade cleanser if the antique porcelain you're trying to clean is a bathroom or kitchen fixture or has stains caused by hard water deposits. Such cleaners, including Scum Cutter and Tilex, can be found at many grocery stores and supermarkets. If the discoloration is many years old, use a commercial-strength cleanser that is safe for porcelain.
Scrub your chosen cleanser onto the discolored areas of the antique porcelain with a non-abrasive sponge, towel or soft-bristled toothbrush. Be careful not to scrub too hard, and wear rubber gloves while you're applying the solution. For stubborn stains, cover the porcelain in the mixture and let it sit until dry.
Rinse the solution from the antique porcelain with lukewarm water. If there are many layers of stains, you can repeat the scrubbing process.