I had the same problem and got much worse when I developed asthma. There are numerous things you can try. However, since it is green you probably should have cultures and/or an Xray done to make sure it's not an infection.
Sinus rinses, exporectants (guainfesin), increasing water intake and exercise have all helped people lower the muscous.
None of that helped me, except massive amounts of water made it easier to cough up (but we are talking 1 1/2 litres straight water, plus juice and tea and food for me who is 85ibs).
What completely got rid of the muscous was high dose omega 3 supplement. I take a 1000mg gel cap (400EPA, 200DHA I think ...) 3 times a day. It did take 3 months to notice anything and I thought it was the weather that was helping,so I stopped taking them and within a week I couldn't breathe and just about needed short course of steroids. Now I'm back on them and everything is settling down. :)
It sounds like chronic non-infectious bronchitis. An excellent mucolytic is vitamin B5. Try taking 500 mg daily. There are no side effects.