Two WP Single Installs – Sign Up to DB1 – Mirrors to DB2?

I want to utilise two separate single wordpress installs. When the user signs up to website 1, i’d like those signup details to be automatically added/replicated to the website 2 database.

So the user selects my_username and my_password as his details. Id like him to be able to log into website 1 and website 2 with those details. Is this possible? (I know about wordpress multisite and it doesn’t work for my project, mainly due to SSL cert complications).

Thanks.