Here are two books. The first one tells what it was like to serve in the RIC. The second is a list of those who served. Neither is about County Monaghan specifically.
Fennell, Thomas. The Royal Irish Constabulary: A History and Personal Memoir. Dublin: [no press given], 2003.
Herlihy, Jim. The Royal Irish Constabulary: A Complete Alphabetical List of Officers and Men, 1816-1922.
John Joseph Harrison (1898-1984) of Co. Monaghan served in the RIC in Belfast. then the RUC. He got shot in the shoulder by an IRA member.