Landlords usually have a green light/red light approach to tenant screening and eligibility. Meet the requirements and you are approved. Fail, and you are denied. Instead of that, think about a 3-tier approval system.
This would be a green light/yellow light/red light system. If 640 is the required credit score to approve a tenant (green light) then perhaps the yellow light zone is 600 to 639. Yellow zone prospects might be eligible if they provide a guarantor, pay a higher rental rate, and/or prepay some rent in addition to having a security deposit requirement. Anyone below 600 is in the red zone and denied.
With this approach, you will obtain more tenants but have safeguards in place for increased credit risks.