Browns, plum, purple, deep khaki, forest green. Any of these colors will bring out the green in your eyes, and make them look even more amazing.
Almost all makeup lines have shadow pallettes out now, for specified eye colors. They provide you with different shades that will bring your eye color to life, and help you save a little money, in comparison to the full sized shadows. A good way to try things out and decide what looks best on you.