To create a private blog readable by only one group, follow this procedure:

1) Create a new blog in the admin console (Blogs > Management > Create * Blog)

2) Click the edit icon for the blog you've just created

3) Click 'Edit Permissions' for the blog

4) Explicitly revoke read access for anyone and registered users (red X rather than blank in the checkboxes)

5) Add permissions for the group(s) or user(s) you want

*note:  write access to the blogs is still through the list of blog authors (you'll see that when you click on the edit icon or when you create the blog)