The names of your family are so common in Ireland that it is practically impossible to find a particular individual. You do have names and a birth for John F. Murphy - hopefully from Tipperary.
There is a not for profit but fee paying History Foundation that has both North Riding and South Riding genealogy offices collections on a data based.
You can search for the son's birth just with his parents names
and the year 1847. Then you don't even need a county/ Once you have his birth record you will have the parish/place as well. www.askaboutireland.ie
Griffith Valuation is used as a census substitute for the year it occurs in 1850. Since John F. Murphy was born in 1847 his parents probably already occupied land.
Their children would also reflex their parents name.
Which would help in a search for her father. Look to name
of their 2nd. son, first son usually named after his father-Michael or grandfather (which also could be Michael if Michael was the first son in that family.
Here is an example of just numbers:
North Riding, Tipperary has 11 Michael Murphy's and 202
Murphy's, South Riding 32 Michael and 371 Murphy's.
No name for the O'Brien's
West Riding 484 and South Riding 151
Now you can see how important the correct county and
parish can be.
Once you have the parish you should be able to look up
the father of Michael and the O'Brien probably belong to the same parish as that is how people met then. If they
were townies they could meet regardless of parish.