To find a job in the Cook Islands for a expat is not so easy. The visa requirements normally state that you have to start a bussiness or buy a existing bussiness in the Cook Islands. One can, if one wants just to move to the Cook Islands and have plenty of money to just live buy a part ownership in a existing business.
There are some places however one can look for jobs.
Working with civil services you can try vacancies at the goverment website: (At the time of writing this there were no vacancies)
This website regulary posts positions: (At the time of writing this there were 7 positions of various character)
You can also look at the following page, they regulary have job positions in the CI.
Few of the companies in Cook Islands is reading that. I would google different resorts and resturants in the Cook Islands and send them your CV directly.