Look for a private landlord and be honest with them. With all of the building run by property management companies you will be denied. They have hold the same standards for each and everyone.
In the meantime clean up your credit.
Call unpaid collections and arrange to pay them off if they remove them. Companies want their money more than the want to lower your credit. Go online to all 3 credit reporting bureaus and dispute all negatives, even it you did them. They have 30 days to verify negative disputes or it falls off. Many of your old creditors may be out of business and will not respond. Get a few things off and you are back in the average range.
Work with a real estate agent. They serve as a buffer between you and the landlord and can ease the way. We have all worked with client's with credit challenges.
Your best bet is to work with a Realtor to sell you and your situation to an independent owner. Large buildings have policies, not compassion.