We're going to buy some chicken wire and hopefully we'll have enough money to buy a lot so we can coat either the inside or outside of the fence in it, I heard that chickens should not be kept in a run with holes wider than an inch. We could probably raise the height with more chicken wire and then use more chicken wire for a roof. Honestly I'm not quite sure what we're going to do, but the roof, whatever it's going to be, definitely needs to be higher so we can stand up when we go in.
We're going to move the shed against the fence in such a way that one door of the shed is connected to the fence, that way we can go in the shed without going in the fence. It probably doesn't make much sense -my Mom had to draw a diagram, it was her idea- but it'll turn out pretty nice if we can set it up. We'll have to ruin the fence though, by cutting a hole in it and attaching it (somehow) to the shed where the chicken door is going to be.
The whole thing will be pretty rigged, and probably a few years down the road I'll have to buy or build an actual coop, but it's a start in my opinion.