OneBody is both a social network and a directory for your church. There are fees for the hosting plans, but if you host the software yourself you can use it for free. If you are looking to have a safe environment for your church members to socialise then this software would certainly be worth checking out.
Some of the features include:
Searchable Online Directory
Take the pain out of printed directories and office calls by letting members share contact details safely online.
Groups and Mailing Lists
Communicate and collaborate with email and group messaging. Share meeting place details, post pictures, track attendance, and more.
Provide a safe and productive social network where churchgoers can share news, pictures, bible verses, and more.
Use OneBody as a tool to suit your specific needs — either as a ChMS or a separately synchronized database.
The free version is open source, and is very feature rich.