I don't have great knowledge of make-up, not sure what eye make-up you can get without mascara, eye shadow and eyeliner (perhaps glitter?) but I found this on a website:
Favorite
eye shadow
shades for green eyes are the earthier tones of each color:
Gold, Bronze, Copper
Brown, Chocolate
Flesh tones, Peach, Beige, Champagnes
Plum, Mauve, Purple, Violet, Pink
Deep and Mossy Green shades
The website briefly suggested you could accentuate green eyes by wearing certain clothing colours (it didn't specify which, but I imagine it'd be similar to the colours they suggest for eyeshadow). Maybe it'd be worth wearing pretty scarves and hair accessories suited to your eye colour?
Not sure if this applies for colour of eyes, but it might be worth remembering that green's complementary colour is red. Maybe that's why people with green eyes often have red hair! So maybe it'd be good to wear a red-shade scarf or hair bow/Alice band. That's just my artsy guess, though!