You can provide clients with the ability to Mark Photos as Private within the Gallery by enabling the Client Exclusive Access feature!
Client Exclusive Access allows you to give clients special privileges such as viewing hidden Sets, and marking photos as Private. Private photos are hidden in the public Gallery and are only visible to you and your client.

How does my client mark photos private?
Once you have enabled Client Exclusive Access, your client will be able to log in by selecting "Enter as Client" and entering the Client Exclusive Access password when they visit the Gallery.
Inside the Gallery, the client can either click on the Privacy Icon at the top right corner of the image, or click on the Mark Private button at the top of the enlarged image view, to mark a photo as Private. Images that have been marked as Private will have a privacy icon on the top left for easy reference.
How do I see what images my Client has marked as Private?
You can view which images have been marked as Private by opening the Collection in your Client Gallery Dashboard, and clicking on the Private Photo Activity section of the Activities tab.