Green diamonds are a result of exposure to radioactivity.
Quote: "The green color is usually caused by the crystal's coming into contact with a radioactive source at some point during its lifetime, and in geological terms, this is measured in millions of years. The most common form of irradiation diamonds chance into is through bombardment by alpha particles which are present in uranium compounds or percolating groundwater. Long exposure to these particles forms a green spot on the surface of the diamond, or sometimes produces a thin green coating which is only skin deep and can easily be removed during the faceting process. But bombardment by beta and gamma rays well as neutrons will color the stone to a greater depth and in some cases turn the whole stone's interior green."
The largest known green diamond is the "Dresden Green". The "Dresden Green" weighs in at 41 carats and 8.2 grams. The gem normally resides in Germany, although it has been on exhibit in the Smithsonian Institute.
For a size comparison, the image below shows the Dresden Green in its usual (rather tacky) mounting.