How do I put 2 (business) directories on the same WP installation?
First, using multisite isn’t a solution to this problem. Each logical site is a single WordPress instance, and Business Directory can only be installed on an instance of WordPress once. Business Directory is multisite compatible, but you must install it as a “single site” plugin right now (network activation is not permitted)
So you can’t install Business Directory more than once per site. But you’d like more than one directory. What do you do?
The simplest solution is to use high level categories to create “two directories” within one master directory. Whether this works with your market or not depends very much on what you’re doing. When you choose to do this, you're assuming that all listings will have the same fields in all categories. BD doesn't currently have fields-per-category (as of 5.0)
One (very complex, unfortunately) solution you might try is a subdomain/regular domain, both with WP installed, both with distinct copies of the Business Directory plugin, and both sites configured with the same content, but the URLs make the user look like they are on the same site. For example:
http://site.com → directs to “main WP install”
http://site.com/page1 → directs to “main WP install”
http://site.com/directory → directs to “main WP install”, “main Business Directory”
http://site.com/otherdirectory → directs to “secondary WP install”, “secondary Business Directory”
OR http://subdomain.site.com/directory → directs to “secondary WP install”, “secondary Business Directory”
This would require a bit of content duplication and some URL tweaks on both blogs so you make sure the users are on the correct site at any time (most of secondary WP site’s links would go back to main WP site, one link on main site would go to secondary site (otherdirectory))…
This second method is recommended only to those who understand advanced DNS mapping and WPMU site configuration. It's not for the faint of heart or weak of stomach.