Die Teckids-GemeinschaftWe are currently establishing our own instance for exactly that and already use it with our community of children. It still needs a bit of help before promoting it publicly.
Apart from that, we also offer e-mail, Matrix, XMPP and cloud storage for children.
If you are interested, let's talk!
GNU social JP is a social network, courtesy of GNU social JP管理人. It runs on GNU social, version 2.0.2-dev, available under the GNU Affero General Public License.
All GNU social JP content and data are available under the Creative Commons Attribution 3.0 license.