A.C.
When my son was a newborn he had a bit of green slime in one of his eyes all the time. Just enough to look gross but it was still there. Our pediatrician said that his tear duct was a little plugged but it would fix itself in a bit of time. If this is something new, your little girl may have some type of cold and you should probably consult your pediatrician. My son is now 2 1/2 and his last bout of green slime (which was coming from his nose-sorry to be gross!) proved to be a warning sign of an ear infection starting.