Brass coatings on bathroom sink and tub drains may wear away over time, leaving unevenly colored drains and stoppers and a persistent ring on the porcelain around the drain. This problem can be caused by abrasive cleaners and some hair care products, especially hair coloring, which can be particularly corrosive.
The best solution is to replace the pop-up and drain assembly. The drains are available (or can be ordered) at home centers and plumbing supply stores. If you want to stick with brass, choose one of the newer types that have a nearly indestructible brass finish. These finishes are applied with an electric charge that vaporizes the brass and affixes it permanently to the drain. All the major plumbing fixture manufacturers make this type of product now.
Or, replace the brass drain with a nickel, chrome or brushed stainless steel drain, which won't corrode and discolor your sink. If you have matching basins, replace both drains.
Also examine the porcelain surface around the drain. If it's scratched or worn (dull), dirt will also cause a ring. Then replace the sink as well.