I have the same problem as described here: Why can I not create an application on my Facebook page?
At the end, there is a solution posted by Kate. I do not know how to implement it. How can I assign a Facebook app created by a personal account to a business page? Does the personal account and the business page have to have the same owner? Can I create an app for my client using my personal account and then assign this app to my client's business page?
There is an option, you can create an app using your personal account, and just assign it to your business page. I had the same problem, it took me awhile to figure out how it can be done. You cannot create an app using the business page. Only your personal account. Best regards