Sadly, not really. But the Republican Movement has set up a website with a mock-election for New Zealand's new head of state. It includes information about the current role of the head of state (and presumes that this will not be changing much), a survey, where it asks for views on the title, term, and method of election, and finally a form where you can nominate a candidate. It was the latter which was most troubling, because despite inclining towards a directly elected head of state, I really have no idea who I'd want to do the job. Recently, we've filled it with judges, retired ombudsmen, and other rather grey public officials, who do it well precisely because they approach it as something like a judicial office, where their job is not to rock the boat, but to do what convention requires. But such people tend not to be public figures. And in real life, they're not likely to seek or campaign for the position, in part because it would undermine the neutrality they need to do their current jobs. In the end, I nominated some elder statespeople with the mana and presumed discretion to pull it off, but I'm not sure I'd want to see the job become a sinecure for former politicians.
So, public nomination comes up against the problem of lack of public knowledge. Which is, I suppose, why in Ireland nominations are done by Parliament and local bodies rather than the general public.
Anyway, once they have enough nominations, they'll winnow them down somehow, then conduct a mock-election using Preferential Voting. So get over there and nominate!