Anyone can wear any color, and green eyes look beautiful with similarly hued liner. If you're worried about being too matchy-matchy, dip your brush into the proverbial eyeliner pool with a matte yellow-green like Tarte EmphasEYES Waterproof Clay Shadow/Liner in Green. These kinds of colors are brightening, but they're also powdery and a little diffuse, so you get emphasis with plenty of subtlety.
For a nighttime shade that's close to black but still has a little bit of verdancy to accent your irises, Yves Saint Laurent Cream Eyeliner in 06 Black Green is a really flattering shade with a smooth texture that looks polished no mater how dramatic you get.
And once you work up the courage to try a little real tone-on-tone, MAKE UP FOR EVER Aqua Eyes in Forest 20L lasts forever, doesn't budge, and makes those baby greens look amazing.