Map from Google - Norfolk_Island

In Norfolk Island, located in the South Pacific Ocean, east of Australia, the climate is subtropical oceanic, with a spring-like weather for most of the year, frequent rains and winds but also an acceptable amount of sunshine. In the warmer months, January and February, the daytime temperature is around 25 °C, that of night around 19/20 °C; the highest recorded temperatures are around 30 °C. In the cooler months, July and August, the average daytime temperature is 18 °C, while lows are around 13 °C. During the winter season, from June to August, the predominant westerlies can bring bad weather, with wind and rain, and sometimes cold air masses of Antarctic origin can bring a little cold at night, with lows below 10 °C.
Here are the average temperatures of the capital Kingston.
Average temperatures - Kingston
KingstonJanFebMarAprMayJunJulAugSepOctNovDec
KingstonJFMAMJJASOND
Min (°C)192019181615131313151618
Max (°C)252524222019181819202223

Precipitation is relatively abundant, so much so that 1,300 millimetres of rain per year fall; there is no real dry season, although in spring and summer, from September to March, precipitation drops below 100 mm per month, while in autumn and winter, from April to August, it varies between 120 and 150 mm per month. The rainfall records are high in all months, which means that sometimes it can rain a lot even in spring and summer.
Here is the average precipitation in Kingston.
Average precipitation - Kingston
KingstonJanFebMarAprMayJunJulAugSepOctNovDecYear
KingstonJFMAMJJASONDY
Prec. (mm)8010090120140130150130909060801260
Days791112121212129978120

Norfolk Island is not exactly in the path of tropical cyclones, but sometimes one of them can leave the tropical belt and head to the south, passing over Norfolk Island before weakening in the colder southern seas. This happens from November to April, but more often from January to March.

Norfolk Island

The sea temperature is warm enough for swimming from January to April, while it becomes a bit cold in the winter months, since it goes down to 19 °C from July to September.
Sea temperature - Kingston
KingstonJanFebMarAprMayJunJulAugSepOctNovDec
KingstonJFMAMJJASOND
Sea (°C)232423232120191919202122

When to go

The best time to visit Norfolk Island runs from September to March, because the rains are less heavy, the sunshine more frequent and the temperatures is pleasant. The warmest months, where you can also swim in the sea, are January, February and March. However, from November to April, and especially from January to March, sometimes the remnants of tropical cyclones can pass. So, the months of September and October can be interesting, being pleasant and spring-like, with daytime temperatures around 19/20 °C, although they are still quite rainy.

What to pack

In winter (June to August): spring/autumn clothes, sweater, jacket, raincoat or umbrella.
In summer (December to February): light clothes for the day, a scarf for the breeze, a sweatshirt for the evening, possibly a light jacket; light raincoat or umbrella.