Would suggest that you check the following websites - they provide all the info there you are looking for, plus you can email for further information.
Cook Islands -
www.cook-islands.com
Tonga -
www.tongatapu.net.to
Both places each has one ISP that I know of, and internet cafes available for public use - at least in the main "cities". Once you get into some of the small towns and villages, it is a very different story.
Both places are magnificent and I do hope your son enjoys them. I have lived and worked in both and can say I thoroughly enjoyed my times there. Coming from your part of the world it may take him a little while to get used to Polynesian time!
Hope the above info helps.