Amazingly, Google has no entries as of yet for “children who blog”. There are, however, several items on “kids who blog,” including this Christian Science Monitor item. Most of them seem to be about teenagers, especially girls.
I mention this, because all of a sudden I now have two kids who blog. It was Elder Son (age 10) who suggested he could have one at something.discourse.net. I didn't like the idea of a blog open to the world, so we compromised on one that will be served from a different second-level domain name, and is password-protected so that only family members can read it. Fortunately my hosting plan allows me to serve several domains for the same price, and I had an underused one hanging around. Younger Son (age 7), who perhaps already has a keener sense about the dangers in the world (he has, after all, experience of dealing with Elder Son…), enthusiastically agreed with this idea.
So now the kids have an online newspaper they can update when they like, and we have an easy way to share digital pictures with a far-flung family. And the non-blogging relatives can send messages to the kids by posting comments. Don't know if it will last as an enthusiasm, but if it does it should be fun.