If your big door is green already I would say tan. We have tannish siding with cranberry trim. Our door is wood but I want to get a new screen door and it will be cranberry color.
Also, we have an upstairs sundeck porch like thing with a door and a screen door. We are going to paint the door tannish and try and paint the screendoor cranberry (we bought the doors before we knew we were getting the siding)