If the words are dark green, the back plate can be ivory white to support dark words.
If the words are light green, the back plate should be as dark as possible, similar to the dark blue close to black. If the background color is too bright, the whole signboard is too "gray" and the text contained is not prominent enough.
In addition, the green used in signboards should not be matched with too warm colors, such as red and orange, which will appear "timid".