If you are talking about the big cover photo (that is behind your profile picture on Facebook) - there are only two options I have found to change it. First, use a computer to access your Facebook account and change that photo.
Or, I have found an app that allows me to easily change that cover photo on the iPad itself. It's called "Fera HD for Facebook." You can get a Lite version, so it's free. It's a bit busy, but since all I use it for is to change my cover photo, I don't mind it.
Maybe it's worth looking into either of those two options?
Marilyn