Someone has already suggested mastadon, but I think Scuttlebutt is a much better solution for what you want. Totally decentralized, persistent, no need for a hosted server. You can set it up in a few minutes and if you're only using it for your small group there's no need to connect to anyone else.
The problem is that SSB isn’t really private. Anything you share in an offline circle of friends becomes public if any member of the group ever connects to a pub server. There is encrypted messaging, but IIRC last time I tried to use it, the threads maxed out at eight people in the client. There are seven people in my immediate family, so I hit limits very quickly.
You can make your own private network that is cryptographically unable to replicate with other networks (like the main net), but I don't think you should ask close friends and family to edit ~/.ssb/config to add a custom SHS key.
As much as I've loved working on Scuttlebutt, I can't recommend using it for this use-case.
