Potential landlords will always make some kind of a judgement call on potential renters, I don't care what the law states. I think the best thing you can do is to sound as professional as possible on the phone and ask them if you can see the apartment/room that is for rent.

When going to see the potential rent, dress appropriately, be clean, shaven, nails clean, you know..the whole gambit. First visual impressions are very important.

Know that even those of us without mental health issues get turned down for rents. I look at it as this, if they don't want to rent to me because I'm on disability for something I'm not willing to discuss and don't have to legally discuss with you, then you are not the landlord for me. If I have good references, look clean, listen well and ask appropriate questions, then what more do they need to know? At least if you are on disability, you have constant income in order to pay your rent. Folks who are working could loose their jobs, they could quit their jobs, they could have to be evicted. You could always play that up as a plus on your end. You can also have a portion of your disability direct deposited to your landlord each month, another great plus!

Keep trying....nothing ventured, nothing gained. We all get turned down for rents and jobs in our lives...it's the nature of the beast. I wish you all the good luck in the world!

ps: I'll bet that room for rent would have been horrid for you anyways, so I think it's a good thing it fell through!