make the gallery offline to everyone but a view new users.
1) Ask users (visitors) to log in to see your gallery. They can see only login page. No need to put it offline.
Config - User settings - Allow unlogged users (guest or anonymous) access.
No
Yes: thumbnail only
Yes: thumbnail and intermediate image
Yes: thumbnail, intermediate, and full-size image
Set it to No.
Advanced settings: Choose from main menu Users - Groups and choose options from the Access level tab.
You have the same options like in Config, but can restrict even other groups.
2)
If you want all your old users to not be able to view your gallery, then make a new group, named it oldusers and set Access level to none. Then move all registred users to oldusers group with phpMyAdmin.
Go in your host control panel - find phpMyAdmin or install phpMyAdmin plugin
http://forum.coppermine-gallery.net/index.php/topic,60908.0.html to have phpMyAdmin directly on your gallery.
In phpMyAdmin click on your coppermine database, click on table usergroups (cpg15x_usergroups or cpg_usergroups) and look at the value (numbers) in group_id for group_name oldusers and Registered (see attachment).
Then click on users table (cpg15x_users or cpg_users) , click SQL (see attachment if you don't see the SQL button) , click Clear and paste:
UPDATE cpg15x_users SET user_group = replace(user_group,"2","110");
Then click GO.
In the code above replace cpg15x with your table prefix. Maybe your users table is named cpg_users or other.
Replace even 110 with the value you have in group_id for group_name oldusers (see attachment).
Registred users should have value 2 just like me.
If you don't know the name for your coppermine database, look in your_gallery_folder/include/config.inc.php
Open config.inc.php and look at $CONFIG['dbname'] =
I attached screenshoots of my steps for moving users with phpMyAdmin.