Adopting from the state has its own set of rules - and it's possible that they may require at least one parent to be a citizen...I can't comment specifically on the laws and/or rules regarding Alabama - but I can tell you, without a doubt, that if you want to adopt domestically (infant, private adoption using an adoption agency, rather than the state) there are no laws that say you must be a citizen.
You can visit
Adoption Directory - Local Services Professional Agency Attorney Facilitator Adopt and contact some of the agencies listed there to see if you'd qualify for their program. Some agencies have different requirements, such as faith statements, age, family size, length of marriage and income requirement.
Good luck with your journey!