After nine months of looking, I finally got a confirmed sighting of a green ringtail possum (Pseudocheirops archeri) in the garden. The green ringtail is unusual in that it does not retire to a nest, tree hollow or roof space during the day, but sleeps on a branch. This one was a few metres up close to the edge of the garden. Unfortunately, it was raining so the photos aren't good. You can see a better picture here.
The green ringtail is a Wet Tropics endemic. It is the only species of Pseudocheirops in Australia. The other four species in the genus occur in New Guinea.