Remove an app from Notification Center preference pane
Open Safari › Preferences › Notifications There you can remove objects permanently by selecting the notification you wish to delete and then either hitting the delete key or by using the remove button ('-') if it exists.
Highlight the desired app and hit delete
I had this problem too. Go to System Preferences > Internet Accounts . You can remove Facebook account from there and then it will no longer appear in the notification center at all
Go to Mail, Contact & Calendars and click on minus sign (-) after selecting Facebook on the left pane.