wpDiscuz Private Comments addon is an easy tool to allow commenters create private comment threads. These threads will be available for website administrators, moderators and for the thread owners. Addon adds a small button next to the comment submit button to set it as private, also it adds [Private] button to parent comments to make it as private after the comment is submitted. The buttons to set comments as private can be displayed / hidden for certain user roles in dashboard. Also, it allows setting certain user role to moderate private comments. This feature can be enabled / disabled for certain Comment Form in case you have many custom comment forms for custom post types.
Please login with some social login button to be able to test the private comment feature. Guests cannot set a comment thread as private.