Do you have any pets? It's possible that your little one has allergies. My daughter and I often have coughing fits for a couple of weeks after, whenever my daughter goes to visit her grandma who has three cats. Also, I had a cough for about four weeks that turned out to be an upper respiratory infection once. I didn't have any green stuff either, so I wasn't very concerned, but I eventually went to the doctor because it wouldn't go away, and ended up on antibiotics. I've had good results from a natural remedy that I've come up with for coughs is a tea made from fresh ginger, honey, a bit of cayenne pepper, and lemon, however, since I don't know how old your child is, I'm not sure about this. If your child is at least two years old, this would probably be OK. Have you taken your child to the doctor yet? I hope this information is helpful, good luck, and Happy Holidays!