To add additional administrators to your organization's Facebook page you must be an administrator and also be Facebook friends with the user(s) that you want to also make administrators of the page.
Log into Facebook with the administrator account and navigate to your organziation's Facebook page. Select Admin Roles from the 'Edit Page' dropdown in the upper right-hand side of the screen.
On the Admin Roles page, scroll to the bottom and click the Add Another Admin link. Enter the name of the Facebook friend that you want to make an administrator.