We visited the Pukaha National Wildlife Centre today. They have breeding programs for native birds which get released in to the wild when the birds are strong enough to cope on their own.
The breeding stock are kept in large aviaries, but the grounds are over 1250 acres and well forested so a lot of wild birds also visit.
These four are all captive birds though:
Brown Kiwi, Kererū (huge native pigeon), Kākāriki and the Saddleback (Tieke).