Any ring which can be made with near-colourless diamonds can also be made with green diamonds. It may be more difficult because of the greater rarity of green diamonds, and the greater problem to find matching stones, but it can be done, with great results.
Three Stones
Fancy coloured diamonds are very effective when used in conjunction with white diamonds. A green centre diamond with two near-colourless ones retains a traditional look. The owner could retain the secret that the centre stone was a diamond while an onlooker might assume wrongly that it was "only" a sapphire.