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.