Could you get some 2x4's and plywood. and put a slanted roof on top. Similar to the roof on this coop. Around the edges you could put some hardware cloth for ventilation.
I have seen people use sheets of tin for the roof. Place a 2x4 underneath on front side to make it slope... Guess you could attach it several ways.....
Most of us "farmers" have a few sheets left over from pole barns or horse shelters. Ask around or advertise on craigslist. good luck!
But..in my kennel coop, I placed 2x4 across the top and screwed them into the metal frame, then I placed corrugated plastic on that. We had quite a bit of snow this year and it held up wonderfully. I used the clear since my girls are in a shady area already.