I had terrible tear stain issues as well. I believe it stemmed from having bad upset stomachs from eating oak tree flowers and having antibiotics for the first 6-8 months we had him.
I tried everything that was suggested from bottled water to commercial stain remover products. When he was neutered they removed 3 remaining baby teeth that had not come out on their own AND they flushed his tear ducts. Nothing worked.
I was at the vet for a check up and I mentioned that I couldn't get rid of the stains. The tech said that a few people had given their dogs Proviable Forte for stomach issues and noticed tear staining had stopped. I told them to give me some.
I gave it to him daily for about 4 or so weeks and noticed that all of a sudden his tear staining had stopped. I had him groomed and they didn't come back. He still has tearing, but they don't stain and a good washing of the area gets rid of them
Another bonus was that he started eating much, much better. Until then he was giving me fits to find something he would eat. Suddenly, he ate his food more regularly, though he's still fussy. But I can live with it.
Give Proviable Forte a try. It's only available from vets - the stuff they sell on Chewy is a different version. I contacted the company and they confirmed it. It's on the pricey side, but I have since cut back to one pill every other day, and the vet suggested I try giving it once a week. I'm not that brave... I'm afraid to going back to staining and not eating