This is a tough one... But there are owners out there that may rent to you. A few things that an owner may consider in lieu of your previous eviction:
1. Larger deposit
2. Pre-pay several months in advance.
3. Have someone co-sign on the lease for you.
These may help your chances but may not guarantee you a home, so I would apply to as many rentals as you can, be honest with the owner and see how it comes out.
You will find a home, you just have to be diligent!
Best of Luck and let me know if you have questions.