As in North America, the arrival of humans in Australia was suspiciously coincidental to extintion of most large land mammals. So possibly they were not sustainable at first, but later arrived at an ecological equilibrium.

Another possible sustainable candidate is Japan, 1603-1867 (Edo Period).
The population remained almost steady at around 30 million for over 250 years.
Wet rice agriculture, soy beans and fishing were the staple means of survival. There was no immigration/emmigration, very little overseas trade, no wars and no epidemics. One could argue that with this population density, deforestation was bound to occur long term, a la Europe. But most of Japan is steep mountains, with much of the population residing in narrow flatish strips. Thus the forests survived in the mountains. Abundant rainfall and a temperate climate also meant the biomass could keep up to a greater extent.

Sustainability surely depends on whether the population can be supported long-term without depleting resources, and on how the society chooses to exploit or protect the resources available to it.