I live in ATL GA where are some private owned communities or apartments that don't do credit checks?

All professional management companies MUST do credit checks - it's their fiduciary duty to the owners. Therefore, any complex or larger building is going to do credit checks - and reference checks, etc, as well. If you cannot p a credit check, you are going to have to find the owner of a small building, or a basement apartment, etc. And have an employment verification letter from your employer, letters of reference, and at least 3 months rent in advance.