So, I do a lot of home repurposing, fabrication, building, restoring and junk just for fun, hobby, necessity or what have you. I have some recommendations just based on my own experience with stuff, and of course past failures. I live in Virginia now, but lived in Louisiana for 9 years. With that hope I have a general idea of what you’ll be dealing with. I can tell you what I would use as far as specifics, but they’re just my preferences. The general type of products remain the same.
So! First thing, I would coat the coop with whatever you choose to coat it with, before you put it together. This will allow you to get between the cracks, inside of seams and offer even coating. Having been one to personally paint AFTER assembly (developing new and creative uses of profanity in the process) I can’t recommend this enough.
As for coating (in your area) your best bet for humidity, rain and UV protection is going to be a penetrating sealer. This soaks into the wood, to create its seal. If you’ve seen something coated a few times with a Poly-type sealant, and after a few years the sealant is still there but the wood is faded, grey or dry looking? And/Or the coating itself is sort of popping or bubbling off? Well that’s why; it’s a coating sealant. It lays on top and doesn’t soak into the wood. So while the water may not soak in, it’s still cooked by the sun and usually still taking on humidity from the air.
I personally like this one:
https://www.ecosafetyproducts.com/acri-soy-concrete-sealer-wood-sealer-1gal-p/a1-3000-1.htm
Another thing I would be worried about, is ground contact. Direct contact with the ground opens your backyard builds to all sorts of new issues and annoyances. Rot, mold, mildew, fungus, bugs...loads of fun right? If you want the bottom footing structure to last for years, putting it directly down on the ground as built is probably not the best option.
If it were me, I would buy wood made for ground contact. Build a footprint frame on the ground, and bolt the coop to it. A footprint frame is just you building basically the bottom of your structure in boards. So it will be a couple of inches higher, but that contact directly to the dirt, is made by something intended and treated for exactly that purpose.
Hope all this helps! If you have any specific questions, let me know.