What does the demon mean when I it says single men not allowed need a..

You have to marry Lady Grey in order to open that Demon Door. (Of-course you can only meet Lady Grey after you have completed the arena quest.)

There are two ways to go about doing this, one of them allows you to both marry Lady Grey and expose her crimes.

The direct approach is to simply do everything she says, and soon you will be married. Then return to the door and he will open.

The second method, which is slightly less direct, would be to talk to the guy in the jail cell once you have gained access to Bowerstone North. Tell him that you'll help him.

Go to the Barrow Fields and talk to the bloke next to the demon door. He'll give you a sob story about a woman he once loved. Ignore all that, and do what he says about flashing your lamp three times next to the stables at the Grey House.

Go into the basement of the house and accept Lady Grey's offer at the end of the cut-scene. You'll get some evil points, but you'll also get the axe. You'll get married, the door will open for you, and eventually the truth about your wife will come out. You won't notice it, though, because she runs away before any harm can come to her.

And, of-course, in Fable 2 she... Well, I don't want to give anything away .

I hope you found this useful.