Facebook Page – Is It Possible to Create an App as a Local Business?

No it is not possible. As stated by a Facebook employee

'Business' or advertising accounts can't manage apps - if you were able to create one as a business account this is a bug or loophole and shouldn't have been possible - only real verified user accounts should be able to create and manage apps.

If you need to share ownership of the app between multiple people you can do so either via making a Facebook Group an admin and adding the other admin users to that group, or by adding the users directly via the API or the 'Roles' tab of the App settings: !Role management popup with 'Create Group' option

You can also specify a business account which will manage the ads for an app in the app settings - on the Advanced tab - but this is effectively the only supported connection between apps and business accounts -

_{Source: http://facebook.stackoverflow.com/questions/10805745/creating-and-managing-a-facebook-app-from-a-business-account}