This site has some great information on causes and cures for eye tears and staining. Depending on what the problem is, different methods work, many puppies will have tearing while teething, and sometimes the problem is resolved with distilled water. A dogs pH can be off, and more acid works on some dogs, (a little vinegar) and some dogs need more alkaline (tums). Joey had a problem with a food, and a food switch helped eliminated the problem. If the area is wet all the time, it's best to find the cause because this can lead to yeast infections.
Tear Staining: The Causes & Cures