I have green eyes as well, and there are a few colors that really complement them.
When you look at a color wheel, you will notice that purple is across from green. That makes it a great choice for eye shadow! If your eyes are a bit close together, you can create the illusion of distance by applying a dark plum near the outside of the eye and lighter purple as you move in.
Stay away from blues; that includes purple shadows that have a hint of blue in them.
2. Gold and Copper
If you are looking for something a little less dramatic than a deep purple, consider applying gold or copper to your eyelids. Finish your look with a brown or gray eyeliner.
Stay away from silver colors and black eyeliner for best results.
If you are looking for a simple daytime look, go with a brown shadow. Because you have green eyes, they already pop, which means you do not need bright colors to draw attention to your eyes.