Register Without Email

Here's a new one! A client of mine has a few patrons that apparently do not have or want to share an email address. Can you believe it? Yet, they have online access, presumably at a library or work computer. The client wants the patrons to manage their contact data online. I'm at a loss how to create an app that requires sign-in but does not use email (zoho accounts)... I know it's not allowed to create a custom authentication system so what's the workaround here?