Map from Google - Nauru

In Nauru the climate is equatorial, hot and humid throughout the year, with constant rains, and without a dry season. It is no coincidence that this small island is located at the Equator. We can still distinguish a rainier period from December to April, when more than 150 millimetres (6 inches) per month fall, with a maximum 250 mm (10 in) or more per month from December to February, and a less rainy period from May to November, when, however, still from 100 to 150 mm (4 to 6 in) of rain per month fall.
Precipitation amounts to around 2,000 mm (80 in) per year. Rainfall can vary from year to year, so that sometimes it can rain a lot even in the least rainy season; however, June is the month that historically has had the lowest rainfall records. The rains occur in the form of showers or thunderstorms, which may be intense, but do not last long, so that the sun has always a chance to shine.
Here is the average precipitation.
Average precipitation - Nauru
NauruJanFebMarAprMayJunJulAugSepOctNovDecYear
NauruJFMAMJJASONDY
Prec. (mm)2802501901901201101501301201001202602020
Prec.(in)119.87.57.54.74.35.95.14.73.94.710.279.5
Days1614131199121411101315147

The average temperature is extremely stable during the year: lows hover around 24/25 °C (75/77 °F), and highs are around 30 °C (86 °F). There is just a slight rise in temperatures between October and December. Sometimes, however, the temperature can reach 35 °C (95 °F), from November to April.
Here are the average temperatures.
Average temperatures - Nauru
NauruJanFebMarAprMayJunJulAugSepOctNovDec
NauruJFMAMJJASOND
Min (°C)242424242525242424252524
Max (°C)303030303030303030313130
Min (°F)757575757777757575777775
Max (°F)868686868686868686888886

Nauru is outside the path of tropical cyclones, because at the Equator there's no Coriolis effect, which is necessary to give life to cyclonic vortices.

Nauru, from above

The sea in Nauru is pleasantly warm all year round, and has a very stable temperature, as can be seen in the following table.
Sea temperature - Nauru
NauruJanFebMarAprMayJunJulAugSepOctNovDec
NauruJFMAMJJASOND
Sea (°C)292929292929292929292929
Sea (°F)848484848484848484848484

When to go

The best time to visit Nauru runs from May to November, being the driest, or rather the least rainy, because showers and thunderstorms may occur even in this period. The period from May to August is the best, because it is slightly less sultry. Since it is not affected by tropical cyclones, Nauru can be visited throughout the year; anyway, the worst period runs from December to February, being the rainiest.
The natural environment of Nauru is still suffering because of the intense mining of phosphates made in the past, and the island is not well equipped for tourism; however, as we have seen the sea is pleasantly warm all year round for swimming and diving.

What to pack

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.