The Royal Irish Constabulary existed from 1816 to 1922. The National Archives hold service records for all Officers and Men. This includes details such as name, age, height, religion, native county, native county of wife, date of appointment, date of retirement and counties in which he served, etc. “The Royal Irish Constabulary: a Complete Alphabetical List of Officers and Men 1816-1822” by Jim Herlihy, gives each man’s Service Number.
Unfortunately I don't have a copy of the book, but maybe some kind RootsChator has, and can help.