Please note that while I've taken pains to add a secure authentication function to Sunrise to prevent misuse, this still opens up the application to external access. This is dangerous in and of itself. Consider yourselves warned. :)

Install the updated Sunrise extension.
In Firefox, add the following preferences, either to your prefs.js file, or using about:config:
"sunrise.password"
"sunrise.hostname"
Both are strings - the password is whatever you want (please don't pick dictionary words :), and the hostname is the DNS name or IP address of the machine that's running Sunrise Desktop. Rememeber to open a hole in your firefall for port 2575, which Sunrise uses to communicate.

Exit Sunrise Desktop application.
Find the Sunrise directoy (most likely "C:\Program Files\Sunrise").
Put the updated sunrise.jar into the Sunrise "build" directory, replacing existing sunrise.jar (if your Sunrise path is the most likely path, this path would be "C:\Program Files\Sunrise\build"). Please make a backup of the old file first, although the new one should be completely backward-compatible. Modify the shortcut that starts Sunrise Desktop to include "-external_access -password yourpasswordhere", replacing yourpasswordhere with the password of your choice. Password must match the one set as "sunrise.password" in Firefox, otherwise you will get authentication errors.
Start Sunrise Desktop.
Enjoy!