jamoros if all the users will be created by yourself, I'd recommend disabling sign in under permissions, and create all user accounts by hand. Then you can also restrict "View discussions" to "Members" and only members will be able to see and interact with the content.
You can use the Create User Modal extension to let you create those new users even when the registration is closed. You will probably also want to use the User Directory extension to easily see which users already exist.
If you plan to have many new users joining the private forum, Doorman as suggested by vaultboy lets you create invite codes and removes the need for you to create the accounts by hand.
