Does the other spouse have good credit? If so, that should make the landlord more receptive. It may be easier for you to rent a unit in a 2-4 unit building from a private person.
Your best bet if you dont qualify for an appartment, which is most stringent , try to rent from a private owner, they will work with you better, and are a lot more flexible, especially if he has property that has been vacant for a while, and make sure the person you are dealing with is actually the owner, or the property manager, make sure you get proof,.
It wont be easy but it can be done, if one says no, go to another one..