Your cat is producing extra tears, probably from a upper respiratory virus or environmental irritant. Then the tears dry in the corners leaving the pigmented discharge. If you have a flat faced cat with prominent eyes, their eyes are always extra exposed.
Check for irritants around the house: hoods on the litterbox, dust, deodorizers in the litter, potpourri, cleaners, carpet fresheners, plants in the house, fireplace or cigarette smoke, etc,
If it's a virus as long as your cat continues to eat and has no colored (yellow/green) discharges from its nose or eyes, the signs you are seeing should resolve in 5-7 days. A virus in the eyes can just become a chronic problem.
If your cat stops eating, develops more significant discharges, or if the signs worsen or persist, call your veterinarian for an examination.
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