There are books listing all of the RIC members. Just try
googling. There are a lot of websites dedicated to its 85,000. members and descendants who have a website as well.www.royalirishconstabulary.comwww.nationalarchives.gov.ukwww.irishconstabulary.comwww.esatclear.ie
(has alphabetical lists)
Start with the above and then let me know as it may help you find more information work with.
With a name such as Michael Murphy - a wife's name or children's name and year of birth would help track the right Michael Murphy. A 20 year spread for birth is pretty big and needs to be refined to about 5 +/- years.
An example would be the 1,326 Michael Murphy's in Ireland
at the time of Griffith Valuations.