Single Sign On for external sites

Hello!

I have a challenge in front of me to create a single sign on into a wordpress site from an external website (different server, different domain, the whole nine yards). Here’s the scenario: a user logs into a real estate management site (non-WP) and then needs to go to a vendors website and be logged in when they get there.

Meanwhile, back at the ranch, usernames and passwords for the non-WP site will be synched via a custom cron script, so that users at the non-WP site will be replicated over to the WP site.

Let it be noted that I have full control of the WP site – but very little or no control at the non-WP site other than maybe some basic HTML in a page.

I am not highly experienced in cross domain single sign on ideas, but this sounds like a pretty tough case to crack. Any ideas?

Thank you!
Scott