If you're looking to take home something other than photographs and memories, here are a couple ideas that you might find interesting.
1. A Cook Islands drivers license. You are not allowed to drive a vehicle in the Cook Islands unless you have a CI government issued license. But don't worry about a time-consuming driver exam, even a blind 4-year-old can get one... as long as he's willing to pay 10 bucks. All that is required of you is to provide the name of where you're staying, stand in front of the camera, and smile. Oh, and hand in your money.
The process essentially is a moneymaker for the government, but, hey, let's be honest, if you're going to deal with government extortion, I'd rather get a neat conversation starter like a foreign drivers license, than just be not-so-subtle demand for a bribe from a police officer. The licenses certainly are worth the money if you get carded, or pulled over for speeding, back at home even once.
2. Stamps. The Cook Islands have an array of beautiful stamps available at the Avarua post office (located near the bus stop in Avarua). Even if you're not a stamp collector, you might want to pick up a couple of these for the quality of the art. My mother-in-law is an avid stamp collector, so we bought several sheets for her. For us, we settled on a beautiful oversized stamp that commemorated the discovery of Aitutaki (one of the Cook Islands) with a scene from the Mutiny on the Bounty. This oversized stamp was $4.20 in local currency... was worth it, I think.
3. The currency itself. Though the Cook Islands uses New Zealand currency, it does have a local coin that features a representation of Tangaroa, the ubiquitous island god whose endowment is prominently displayed. Certainly a conversation starter back home.