I had a completely white bulldog with black spotted skin. He had dark tear stains running from his tear duct area down. I tried a few of the tear bleaching products sold for dogs but none worked (besides being expensive). I also tried some suggested home remedies (e.g. hydrogen peroxide, etc.) and those were not effective either. A vet told me the tear stains were caused by the acidity in the dogs system and if I neutralized his system, the stains would go away.
His suggestion was to put vinegar in the dogs drinking water! He suggested putting just a "tiny" bit of vinegar in the drinking water for a few days (I interpreted that as about 1/4 of a vinegar bottles cap full) and then increase the amount of vinegar added until I was adding about a teaspoon to the drinking water each day (I would estimate his drinking water bowl to contain about 5 cups of water.) Each time I changed or added water to his bowl, I also added the vinegar. Within a few weeks, the tear stains were gone for good!