I think blue and petrol hues goes very nicely with green eyes. One shade that I have really grew fond of is Orbit from Sleek's Ultra Matte V2 palette. I actually don't have anything like it in my entire make up stash, which is quite a lot!
So try it out, I promise you won't be disappointed!!
Primer - NYX JEP in Milk
Shadows - Sleek V2 Palette (Orbit & Ink), Sugarpill Pressed Eyeshadow in Tako, Mad Minerals Multi Use Mineral Colors in Whisper Mint, MAC Eyeshadow in Surreal
Eyeliner - MAC Fluidline in Blacktrack
Eyepencil - Kiko Color Kajal in 109 Blue
Mascara - Eyeko Curvy Brush Mascara
Eyebrow - Illamasqua Fine Pencil in Peace with Yaby Brow Shade No.2