I spent two years in England teaching riding over 40 years ago. The English are terrified of draughts on their animals. All horse boxes ( stalls) only have windows on the same side as the box ( stall) door.The window is only hinged at the bottom, and opens out, placed high up on the wall.. It is called a Sherringham window. It directs air up, and over, an animal's back , not in to it. On the coldest days, when horses would come in from the fields with icicles on their whiskers, those windows were never closed, nor were the top doors. You simply added more rugs ( blankets ) to a clipped horse. NO colds, coughs etc, I learned to fear the damp draught. I put Sherringham windows in my coops. They work beautifully to ventilate it in winter, with no build up of moisture, and in summer in S.C., with a low opposite intake window , exhaust the heat from the coop.Galanie, I understand what you are saying and it makes sense, but in my case the metal roof gets condensation in the run area too - which has hardware cloth screening on three sides of the structure. That doesn't make sense to me, but it happens. My shadecloth ramada (shadecloth "roof", not a solid roof) also gets condensation on those same mornings. So does the side of my house. So maybe it's partly an air movement thing. When the air is still it condenses on surfaces with a temperature differential. We get a lot of radiational cooling here in the desert. Still air and no cloud cover = lots of radiational heat loss = lots of temperature differential on top versus bottom of a relatively flat roof, or outside versus inside of a house. Throw in a little humidity and you get condensation on virtually everything.
The roof on your coop has more slope than the roof on my coop/run. I'm wondering if that makes a difference. If the coop is designed so the heat of the chickens causes an upward air movement, and the roof is designed to direct that air movement up and out, maybe it's the chicken heat that creates enough convection to move the moist air up and out of the coop even on a still air day... and maybe my coop/run is so open there's not much convective process going on... which may be aggravated by the fact that I don't have many chickens in the coop, either... Just speculating, trying to figure this out before I build my next coop.
Was going to make a plywood/rolled roof instead of a metal one next time, but then I took a rainwater harvesting class and they said if I wanted to use the water for the chickens I'd be better off with a metal roof. So I'm back to figuring out the condensation thing again...Will definitely add more slope and more open-rafter space for the coop roof next time, but I'm not sure what to do about the run.
I like the half-monitor designs that have been posted. I'll probably do something along those lines for the next coop project. I'd repost the links but they've gone missing.