This is a class that is coded: No Publish Register.
This coding will make the class hidden/invisible to the general public (who may be browing the course catalog, searching for key words, etc).
What you (as the administrator) can do then is copy the URL to this class (using the Copy Link to Course Status page) and then share that link (imbed in an email) that is sent to JUST the folks whom you would like to have the ability to see the class and enroll in it!