NIWA have some very useful resources, including information about king tides:
High perigean-spring tides, colloquially known as “king tides”, peak 1–2 days after New or Full Moon when Moon is in its perigee (i.e., when it is closest to the Earth during its 27½ day elliptical circuit around the Earth), but dates of highest tides vary around New Zealand.
In 2020 the Moon’s closest perigee occurs on 8 April* and coincides exactly with a Full Moon, with next closest on 17 October (New Moon). The year’s highest high tides will occur in the two perigean phases of February to April and August to November.
For the year 2020, “red-alert” dates cluster around very high tides (perigean-spring tides) that peak 1–2 days after New or Full Moon when Moon is in its perigee and “carefree” dates cluster around lower high tides after First or Third Quarter when Moon is close to its apogee.
Download the 2020 calendar for Taranaki (160 KB PDF) or just check the screenshot: