Black water stains on wood are an indication that the stain has penetrated through the protective clear coat. This type of stain requires more work to remove it, but it is not impossible. Black stains are often caused by condensation from drinking glasses set on wood tables or from pet urine on hardwood floors. Removing these stains involves sanding, bleaching, re-staining to match the existing stain and applying a clear coat.
Cover the areas around the stain with painter's tape and plastic to protect them from the stain removal chemicals and allow you to work on the stain without fear of spreading the chemicals too far.
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Sand the surface of the stained area to remove remaining clear coating and stain. Sanding will prepare the damage to absorb the stain removal chemicals. Sand only in the direction of the wood grain. Sanding against the grain creates scratches in the wood and more work for you.
Pour a small amount of hydrogen peroxide into a plastic container that you can throw away. Apply the peroxide to the stain with a paintbrush, and allow it to set overnight covered with a rag moistened with hydrogen peroxide. Remove the rag and allow the treated area to dry.
Sand the treated area lightly after it has dried. Apply more peroxide if there is still a sign of black discoloration. Allow the peroxide time to work, and sand it again. Use a wood bleach for a more aggressive approach if the hydrogen peroxide does not work.
Apply matching stain to the treated area when the stain is completely removed. Allow the stain to dry overnight, and apply a clear coat of polyurethane over the stain. It is best to apply two coats of polyurethane.