It is typically tropical weather in the Cook Islands.  The rainy season, Summer, starts in November and lasts until mid March or early April.  It is quite hot and humid during this time with frequent afternoon downpours.  The increased humidity also means more mosquitos; especially prevalent in the morning and early evening hours.  The sun usually shines in the morning but afternoon rain is quite common.  Cyclones are formed during this time of year as well, but on average the Southern Cook Islands experiences a proper cyclone once every 8 years or so. 

Winter begins after April which cools down the humidity considerably.  This period lasts 'til November and is much drier.  Aitutaki and the northern island group are warmer than Rarotonga year round.  The water temperature is also cooler during the winter months.  Average temperatures during these winter months are about 26C, and may even become a little cool at night at 19/20C.  

Traveling to the Cook Islands from late March through to  November will offer the best of both worlds....warm, sometimes humid but not horrible, and with long sunny spells and occassional tropical rain.  Using this weather information is just a guide as things do change from year to year depending on the southern oscillations and alternating La Nina/El Nino weather patterns.  Some years are more rainy than others so checking historcal weather can be useful.  The following website contains historical weather for all destinations:

For those interested in keeping up with the weather and potential storms in the Cook Islands and the South Pacific in general here is a satellite web site that shows the Cook Islands, French Polynesia, Fiji, Samoa, Tonga, New Zealand as well as others. The island of Aitutaki is the small dot located just east of 160W and just north of 20S. Rarotonga is located due south of that just below 20S

For visitors wanting to check the local weather forecast for an upcoming trip this is a link to the Cooks Islands Met Service site.