Okay, so I found a solution that will work in my case with the recommendation of Michael.
Since this is a new site that does not actually have any members yet I set the first blogs wp-login page (www.website.com/blog/wp-login.php) to redirect to the members only blog (www.members.website.com/wp-login.php) using this simple php script:
<?php
header( ‘Location: https://www.members.website.com/wp-login.php’ ) ;
?>
so that when they register they are really registering for the second blog. Then I used the plugin “Members-Only” to hide the content from non-members.
Hopefully this helps anyone in the same situation!
Tom
