Hi Misty, Welcome to BYC, Alabama, (repeat after me, "Rooooooooooollllllllllllllll TIDE! Roll!) and the ALABAMA!! thread.
First of all, make a flyer that has your requirements for the rental you want. Make a list of 'MUST haves,' (permission to keep chickens, minimum size, rent amount you want, etc.) and a list of 'wants' (existing coop, or outbuilding that can be converted, swimming pool, you know, things that are negotiable
) and be sure to mention that you are stationed at Maxwell.
Then, contact the local feed stores, farmers markets, and vet offices in the surrounding communities. Ask them if they know of anyone that has rental property like you want and if you can email or fax them the flyer for them to post on their window or bulletin board.
See if you can find a realtor to help you, but negotiate a commission fee for the realtor, first. Remember to research area schools, if you have kids. There are some school zones that you don't want to be in, with or without your chickens.
I am not too close to that area, but I will help in any way I can. I think Razadia is, and there is another BYCer or two near there, so maybe they will chime in and help.
Good luck and keep us posted.
ETA: BTW, where are you moving from?