[Starring_Emma]

How big would their house have to be for just 4 or 5 of them.  How do you keep the raccoons, coyotes, hawks and eagles from getting at them if they're out in the yard?  How do you get them to go back in their house at night before the coons and coyotes come out?  What do you do with them in the winter when it's 20 below zero out?

[too many girls]

sorry i can't answer your questions, i don't got racoons or coyotes (thank god) just plain old Mr Fox.

[poultrygeist]

Over here, we reckon on about 1 sq ft per average chicken in the house. If you made the house about 2ft x 3ft, you'd have enough room for 5 banties, which are smaller than normal hens.

As TMG says, we don't get much more than foxes and badgers. If you keep chicks, there's a danger from magpies and some birds of prey.
Hopefully one of our American members can advise on your native wildlife. It would be interesting to know.
A fox proof run needs to be made from steel mesh on a timber frame, similar to an aviary. They are good climbers (like racoons I should think) so the top needs to be mesh too.
That would keep birds out but would mean keeping them in a smaller area.
Maybe you could tie some string between posts above head height so they can't swoop down.
Just need to worry about the racoons and coyotes then 

Rob