Cosigner for tenant screening

[Raghavendra Jakkani]

I got an application for rental and the credit score was below 600 and I am looking for score above 650. The applicant said they can pay 2 months rent as deposit and first month rent. They also said they can get a cosigner on the lease who has good credit score.

What are the risks of having such a tenant? I will be of course checking other factors such as employment, criminal and eviction history of the tenant who will be staying. 

What should I check for the cosigner other than credit history?