Recycle. We framed our entire coop with wood from a deck that was removed from the back of our house. You could do the same by watching for any consturction in your area and ask if you can have any discarded lumber. The other way would be to find a shed or playhouse in the classifieds, ebay or Craig's list real cheap and convert it. Good luck!
I'm working on a small coop right now that I am building from old pallets. It's kinda rustic looking because of the wood and how I'm overlapping the boards. But other than the nails that I bought and whatever I decide for the roof it's been free.
Pallets...You can go to UTube and look up pallet sheds or how to take apart pallets. Found several ways to do it. Looks simple enough, Just have to find yourself some free pallets. Lots of people say look at Tractor Supply. I live in a small town so i'm limited on where I can get free pallets. But it hasn't stopped me yet. I just got my first bunch for pallets today. I would be building right now but its raining today.
I'm excited to use the pallets. I agree with paddock36 it gives it a rustic farm feel. You could try looking on craigslist, there is always free wood or pallets of some kind when im looking. Good luck!
house construction sites, co-workers, a local used building material reseller, etc. i am almost done with a 4x8 coop on stilts with a 3' wall in the back and a 4' wall in the front. everything but the siding was donated to me. lumber, plywood, and OSB came from co-workers' old projects. more lumber came from 4 big pallets that my employer was about to give to someone to burn for firewood. tar paper and shingles came from a co-worker whose house was re-roofed this past summer, and the old leftover shingles didn't matcher her new roof. windows were given to me by a friend. insulation was robbed from a couple of houses under construction down the street from us. after searching hi and low for free or recycled siding, i broke down and bought some new T1-11 siding at a local lumber yard.
long story short - look around. we'll have about $74 in our coop, and that is exactly what the siding cost us yesterday. i know if i can do it you can.