Tom, the worst are Black and Grey-headed Flying Foxes. These mega bats smell the fruit as soon as they start to turn even a bit yellow. They are like exocets focussing in. You have to bring the fruit in as soon as it starts to mature. The bats also damage the green fruit with their claws while hanging there having a munch on the ripe fruit.
Birds can be a problem. Friarbirds have featherless heads that are ideally suited for getting right inside large fruit. With no feathers the plumage doesn't get matted from the pouring juices. In the north, Helmeted is a big problem but the Noisy Friarbird here in the south prefers blooms more.