Along with Sean Kenny (Lund), I've written a working paper looking at the stability of Irish banking from 1797 to 1826. The paper is entitled "Wildcat Bankers or Political Failure? The Irish Financial Pantomime, 1797-1826". You can access the paper here at the Queen's University Centre for Economic History website.
Abstract: Using a new biography of banks, we examine the stability of Irish banking from 1797 to 1826 by constructing a failure rate series. We find that the ultimate cause of the frequent and severe banking crises was the crisis-prone structure of the banking system, which was designed to benefit the political elite. There is little evidence to suggest that wildcat banking or the failure of the Bank of Ireland to act as a lender of last resort were to blame. We also find that the main economic effect of the episodic crises was major diminutions in the money supply.