Joomla requires an email address for user account creation. We can't bypass this behavior as it's hardcoded into Joomla user management.

So the only solution is to randomly generate fake email addresses for them, which is doable using CB Auto Actions. That topic is how you'd do this. What about that solution didn't work for you? You'll need to adjust the PHP to generate random emails of course, but that should work. Be sure you set the email field to not display on registration or profile edit as well to remove the field itself.