Joey had bad tear staining when I switched foods once, and it lasted a few weeks after we switched back, so it can take a while to completely clear up if food is the culprit, but I noticed a huge difference right away. Other dogs can handle the food that Joey had just fine, so it’s more about what your dog is allergic to. It could be environmental allergies as well. I agree with Megansmomma, growing the hair out can make a difference, no more short hairs to poke the eyes and cause tearing. Here’s a good article on tearing the causes and cures.
Tear Staining: The Causes & Cures