Virtually every state has a "Right to Farm" law, certainly every state I've looked at, and quite possibly all of them now. And not a single state whose right to farm law I have looked at does what most people think it does.
Alabama is no exception.
Ala. Code § 6-5-127 (2013)
Here, I'll help...
and then you will find things like this:
I did NOT search the whole of the code, that was just a quick hit. There may be exceptions for smaller than commercial scale coops. and be aware that "Chicken Coop" is defined in the code, as is "urban farm".
You could search your Zoning. You need to know how you are zoned - your tax rolls will tell you that, and if you are actually in the city, in a special taxing district, or not. Because the zoning officials can tell yu whatever they want, and you can't rely on it. Unless its in writing, and...