I can’t see it on my blog right now, but I’m pretty sure it’s just a tick box for ‘users must be logged in to see posts’.
Failing that, you could do a check in index.php
to see if there is a logged in user, and if not display an error message and the login screen. In fact, you could just run that check anyway if you were to specify the post ID’s that you wanted for that.
Or even take it to the next step – copy index.php and rename it, give it a template name, and add some code to check if a user is logged in then. You’d need to install the ‘Custom Post Templates’ plugin, and then all you do is select the template for private posts on the ones that you want to only be visible to logged in users.