Go meet them and talk; tell them your story and don't lie or exaggerate, be honest and open.
If they won't rent to you, you probably didn't want them as a landlord anyway.
Good luck and may God bless
Since we don't own the properties that we list for rent we follow the owner's instructions or present the application for the owner to make a decision. My experience has been that those that use realtors overall prefer higher credit scores but depending on the property some owners may be more flexible.
Individual owners that use other services such as craigslist, hotpads, etc. may be more understanding in regards to your specfic situation since the economy has forced many people to be "right sized", downsized otherwise known as laid-off or fired.
Write up a letter of explanation with previous landlord references and be prepared to perhaps pay additional security deposit to make the owner feel more secure about leasing their property to you.
Best of luck in your search.