http://www.ck/ calls itself the definitive Cook Islands website. I wouldn't argue...go and have a look round. It's outstanding. There's everything from advice on getting married in the islands, to investment opportunities and bereavement notices! And that's on top of all the information about the islands themselves.
And the population information you see on each island page is derived from the 2001 census and is published on
http://www.citypopulation.de/Cook.html