I am bumping this up since no one replied. I am still having problems with facebook, instagram and other apps not pushing, or only push without sound. Maybe someone figures out what the fix is. It cant be a facebook thing if alot of my apps, email and text dont have sound. And apple swapped my phone out, so it cant be just the phone.
This is not a jailbrake solution or alteration to any default software. This is using the factory settings to turn this feature on so that your Facebook push notifications will work on iOS 6.
I solved this on my iPhone 5. It would work for 4 and 4s as well. I think this will work for the iPads too. So go through the steps and try it out.
First make sure this is done so that you can go on to the actual solution. Facebook push notifications are controlled inside the actual Facebook app under Account Settings>Notifications. They are NOT controlled under the iOS Settings>Facebook>Settings>Notifications, if you go there you will be directed to the actual Facebook app.
Now its time for the solution to the problem. There is one more step that you need to do that doesnt turn on by default for some reason.
1. This starts from your iOS device home screen
5.Turn on the Notification Center required to have the push notifications work
6. Under Alert Style by default this is set to None for some reason. So, turn this to the style you want.
7. Turn on the Badge App Icon if you want to, this will display the number of new notifications on the Facebook icon, just like it does on your Messages app when you have a new text message
8. Turn on Sounds if you want to, this will play a sound when a new Facebook notification comes in
Well that is it! I hope you enjoy receiving your Facebook push notifications on your iOS 6 device now.