Map from Google - Tonga

In Tonga, Oceanian archipelago that lies south of the equator, the climate is tropical, influenced by the trade winds, with a hot, humid and rainy season from December to April, and a cool and relatively dry season from June to October. In the northernmost islands, also May and November are hot and rainy, and even in the cooler months the temperature is high; on the contrary, in the southern islands, May and November fall within the relatively dry season, while the period from June to September is pretty cool. However, even in the relatively dry season, throughout the country brief showers and thunderstorms may occur, which fortunately do not reduce too much the sunshine hours. Generally the rainiest month is March.

In the northernmost islands, which lie at a latitude of about 15° (Niuafo'ou, Niuatoputapu and Tafahi), the climate is hot and humid all year round, so that we can speak of equatorial climate: between the warmest months (February and March) and the least hot months (July and August), the difference is little: the maximum goes from 88 °F to 84 °F.
Here are the average temperatures of Niuafo'ou.
Average temperatures - Niuafoou
Min (°F)757575757573737273737375
Max (°F)868888868684848484848686

The annual precipitation is abundant and exceeds 90 inches, with a rainier period from November to April, when it exceeds 8 inches per month, two transitional months, May and October, with 6.7/7.1 inches per month, and a less rainy period from June to September, with 4/5.5 inches per month. In this area, therefore, the best period goes from June to September, being the least rainy, and albeit slightly, the least hot.
Here is the average precipitation.
Average precipitation - Niuafoou
Prec. (in)129.8129.

Further south, in Vava'u and the surrounding islets, the annual rainfall decreases to 83 in, and even the temperature in the cooler months comes down a bit: the maximum drops to around 81 °F in July, August and September, but it's still warm enough for a beach vacation, so here too the best period is from June to September, when however the rains are around 4/4.7 inches per month. Here are the average temperatures in Vava'u.
Average temperatures - Vavau
Min (°F)737575737270686870727273
Max (°F)868888868282818181828486

The sea is warm all year round for swimming, reaching a minimum of 77 °F in August and September.
Sea temperature - Vavau
Sea (°F)828282828179797777798182

Further south we find the Ha'apai group, comprised of islands as Lifuka, Foa, Ha'ano. Here the rainfall drops to around 63 inches per year, at least in the flat islands, because there are also volcanic islands, such as Kao, with inland slopes that enhance the formation of thunderstorm clouds.
Here is the average precipitation in Lifuka.
Average precipitation - Lifuka
Prec. (in)

The maximum temperatures range from 86 °F in February and March, to 79 °F from June to September. Being the relatively dry season a little longer, here the best time is from May to October. Here are the average temperatures.
Average temperatures - Lifuka
Min (°F)757575737270686868707373
Max (°F)868686848179797979818284

In the far south, we finally find the group of Tongatapu, where the capital Nuku'alofa is located, and the group of 'Eua. Here precipitation is still around 63/67 inches per year, but for the more southerly position (they are a latitude of 21 degrees south), winter begins to be a cool season: the maxima from June to September are around to 75/77 °F, and sometimes cold air masses, able to drop the temperature by a few degrees, can arrive.
Average temperatures - Nukualofa
Min (°F)737575726868646466687073
Max (°F)848686848179777777798284

In the southernmost islands even the sea temperature drops to 73 °F in August and September, therefore it remains acceptable but not so warm. Given that the minimum temperatures remain generally high, at around 64/68 °F, the conditions remain usually acceptable, but for those who are sensitive to cold, it could be a little cool. So in these southern islands of Tonga, you can choose the months of May, October and November, when the daytime temperatures are a little higher, at around 79/82 °F.
Sea temperature - Nukualofa
Sea (°F)818181817977757373757779

The islands of Tonga are in the path of tropical cyclones, whose season runs form from November to mid-May, although they usually pass from December to April. A particularly intense cyclone that affected Tonga, was Ron, which hit the northern islands in January 1998.


When to go

The best time to travel to Tonga goes from June to September in the northern islands, up to the group of Vava'u inclusive, from May to October in the Ha'apai group, and finally corresponds to the months of May, October and November in the southern group of Tongatapu.
Anyway, considering that, albeit rarely, cyclones may occur even in November and the first half of May, to be sure you can exclude these periods from the planning of the trip, even where they are part of the best period.

What to pack

For the northernmost islands, all year round, tropics-friendly, loose fitting clothing, sun hat, a scarf for the breeze, a light sweatshirt for the evening, light raincoat or umbrella.
For the central and southern islands:
In winter (June to August): light clothes for the day, a scarf for the breeze, a sweatshirt for the evening, possibly a light jacket for the southern islands; light raincoat or umbrella. For the reef, equipment for snorkeling, water shoes or rubber soled shoes.
In summer (December to February): tropics-friendly, loose fitting clothing, sun hat, a scarf for the breeze, a light sweatshirt for the evening, light raincoat or umbrella.