According to his Wikipedia page, Joyce was born in 1967 in New South Wales. However:
His father, James Joyce, was born in New Zealand and moved to Australia to study veterinary science at the University of Sydney, where he met Joyce's mother, MarieThe Guardian has some links here and a conviluted explanation about the Citizenship Act 1977 (as enacted) and claims to citizenship by descent lapsing. But the descent clause of that Act only applies to those "born outside New Zealand on or after 1 January 1978". Joyce was born before that, so his existing rights of citizenship were protected by s13 of the Act, which makes it very clear that everyone who was already a citizen stays one, and (to reiterate the rules of the British Nationality and New Zealand Citizenship Act 1948),
every person born outside New Zealand on or after 1 January 1949 but before 1 January 1978 shall be a New Zealand citizen by descent if... in any case, his father was a New Zealand citizen at the time of that person's birthJoyce's father was a kiwi, so he is a kiwi, end of story, no registration required. Which means that he will lose his seat in Parliament. That seat is the Australian government's majority, so NZ citizenship law may very well have just caused an Australian election.
Edit to add: Joyce is apparently trying to argue that his father wasn't a New Zealand citizen because we didn't create a citizenship until 1948 and before then everyone was a "British subject". Unfortunately that doesn't help him. Section 16(1) of the British Nationality and New Zealand Citizenship Act 1948 is crystal clear:
Joyce's father was a British subject immediately before the date of the commencement of the Act. He was born in New Zealand. And so under New Zealand law he became a New Zealand citizen, whether he knew it or not.