Thanks for replying.
This discharge is symptomatic of infection. If attempting to treat at home you want to be very careful first of all that the eyes continually looks better through treatment, and no signs of rubbing at it, reddening even worse, or cloudiness appear in the eyes.
You should rinse the eyes with sterile saline, like that found in regular contact lens solution, and do not let the tip of the container touch the eye. Make sure it is not the disinfecting/storing type of contact lens solution, just the normal saline/ NaCl. You can wipe around the eyes with the saline soaked on a soft cotton ball or gauze, but don't use anything harsh like paper towels.
You can also find a pet safe ophthalmic antibiotic ointment at most pet supply stores, catalogues, pet stores and some pharmacies: like terramycin, triple antibiotic (neo/poly/bac), etc. Ask the sales people if you need help, but it does need to be safe for the eye, not a topical one for skin. After rinsing the eyes, apply the ointment 3 times a day (every 8 hrs) for 10 to 14 days.
It can also be bought online, here is a link of just one sight that sells it, if interested:
This is likely conjunctivitis, but could also be a scratch or ulcer forming and if not starting to clear up in a couple of days, you'll need a vet to check it. It is also very possible some debris or dust settled in your dog's eyes, causing this problem.
Best of luck, and let me know if I can help further.