Small Business Stability Act This bill allows the Federal Deposit Insurance Corporation (FDIC) to guarantee an insured depository institution's uninsured deposits in noninterest-bearing transaction accounts for a single period not to exceed 60 days without complying with requirements to minimize cost to the Deposit Insurance Fund. This authority requires (1) written recommendations from the FDIC board and the Board of Governors of the Federal Reserve System, and (2) a determination from the Department of the Treasury that this step would avoid or mitigate adverse effects on the stability of the banking system.