I found a rental for a couple with 5 kids, a dog and a foreclosure. We put together an explanation to the landlord and set up a meeting for them to meet. They have been living in the house for 4 years now. Everyone is very happy.
As a landlord for over thirty years and a Realtor for 15 years, I find honesty is the best way to go. I rented to a couple who were engaged coming off (both) a divorce that wrecked their credit score. They came to see the house with pay stubs and an explanation of what had happened. I took a chance with them and they are excellent tenants. If you get caught in a lie it is over, honesty is the way to go and I am assuming you have a legitimate story to tell