The Carboniferous, like the Silurian Era, seems to have passed New Zealand by, leaving it relatively unscathed. If so, there's some explaining to do, for elsewhere in the world, the long Carboniferous Era has had a substantial impact.
It began as a time of extensive estuarine and coastal marshes in tropical climates, where decaying vegetation accumulated, ultimately to form the deep seams of coal and oil which have given the era its name. In large areas of the world, also, there were shallow, reef-dotted seas, where limestone formed. Later, the climate cooled and sea levels fell, until widespread glaciation set in. And all the time, the continents were shifting under the influence of plate tectonics. Early in the Era, Africa and Euramerica joined, throwing up the southern Appalachians, while South America moved northward towards North America. Gondwana, meanwhile, headed south towards the southern pole. By the Late Carboniferous, the Tethys Sea had closed, and Africa, Euramerica, South America and Gondwana had merged to become the huge Pangea super-continent. By then, Gondwana lay over the South Pole, and glaciers developed across much of Antarctica, central South America, South Africa and Australia. The ice age is estimated to have lasted for some 90 million years, well into the succeeding Permian.
So what was happening in New Zealand while all this was going on? In terms of rock formation, it seems, very little. The 1:2 million scale Geological Map of New Zealand is blank for this era; all the legend carries is a note stating that 'Outcrops in Nelson, Canterbury and north Otago are too small to show.' The outcrops not shown in the Nelson area are small indeed: a tiny area on the tip of Pepin Island composed of coarse-grained granodiorite and granite, which have been dated on the basis of inclusions contained in zircon crystals to 310 million years before present. Otherwise, nothing.
Two possibilities exist to explain the near absence of Carboniferous rocks in New Zealand. One is that they exist, buried deep beneath younger strata. This is feasible, for the geosyncline in which the Permian rocks of Zealandia collected was almost certainly in place earlier. Beneath the Permian there are also several thousand metres of basic volcanic lavas, conglomerates, breccias and tuffs, as well as igneous rocks, which may be at least partly Carboniferous in age. In this case, the tiny outcrops seen at Pepin Island are just the tip of a very large iceberg. The other possibility is that the Carboniferous was a period of net erosion, and any rocks that formed were stripped away, perhaps with others from the Late Devonian and earlier. This, too, is plausible, for as Gondwana wandered southwards, and sea levels fell, any land exposed in Zealandia would have been subject to active weathering and erosion in cool or cold climate conditions. Where the products of erosion have gone, in that case, needs to be explained.
Which, if either, hypothesis is correct is difficult to say without more evidence. Meanwhile, the story of the Carboniferous in New Zealand remains unresolved. But if you want to see any firm evidence of the Era, you need to head for the coastal cliffs on Pepin Island.