Have you heard of Blue Moon! I has nothing to do with the moon being the colour blue. Rather it deals with some cosmological counting of months and cycles of the moon. But I heard in the near future people actually paint the moon blue with lasers and a neat light show when it does happen.
But what about a Green Moon? In this case a Green Moon is when there is a New Moon (when the moon goes 'unlit' by the sun) and it happens to fall on New Years Eve. Thus the first Day of the New Year is synchronized to the first really new new years moon of January 1. Thus that moon is Green Moon.