If humid heat is your issue I suggest considering a monitor roof on the coop. My little, in-town coop was never any hotter than the outside because of the excellent ventilation a monitor roof provides.
It's harder to build than a simple shed roof, but a reasonably competent handyman should be...
OK, from the perspective of a person whose daughter works in and late brother-in-law worked in engineering and whose father believed that anything that couldn't be expected to last 50 years was a temporary make-do, ....
How long do you want it to last?
What kind of snow and/or wind loads do...