Get Your Dog Care Questions Answered by Experts
This could be a number of issues ranging from turned in eye lashes to inner eye infection to corneal ulcers etc.
I'd plan on seeing your vet about this as with the green discharge that is typically a sign of infection.
You can read about the eye issues in dogs here to see a variety of problems
What your vet will do is look in the eyes, perhaps stain them, check eye pressure and determine if this is injury, infection, a pressure problem etc and then prescribe the right meds to clear this up or perhaps suggest surgery if the problem is something such as entropian (see above article).
You can use sterile saline to clear the eyes of debris but you really should see a vet about this problem.
Hope this helps you!