That is a reference to the townland of Garryadeen, which was located in the civil parish of Grenagh. A Google Map shows that Garryadeen, by the shortest modern day route, is 18.5 miles southwest of Castletownroche: https://is.gd/0SGTnX
In a book by Brian Mitchell called, "A Guide To Irish Parish Registers," one of the Catholic parishes located in the civil parish of Grenagh, was also named Grenagh. According to the National Library of Ireland, the Grenagh Catholic Parish baptism and marriage registers begin in 1840. See: https://registers.nli.ie/parishes/0058
The 1854 Declaration of Intention for John Herlihy that you attached, shows he was born on 24 June 1826, which means there would not be a baptism record for him in the Grenagh parish registers or a marriage record for his parents.
There was also another Catholic Church Parish in the civil parish of Grenagh, according to Mitchell's book. This was the Catholic Parish of Mourneabbey. This parish has baptism and marriage records back to 1829. These parish registers would also commence too late in time to have recorded John Herlihy's birth in 1826.
Go to the following Library of Ireland link to see the availability of the Mourneabbey Catholic registers, and to also view a Catholic Parish map, showing that Mourneabbey is just north of the Catholic Parisdh of Grenagh: https://registers.nli.ie/parishes/0083
Another Google Map shows the locations of Garryadeen, Grenagh, and Mourneabbey in County Cork: https://is.gd/txaELb
For a Google Street View of rural Garryadeen, go to: https://is.gd/O35gQs
The Catholic Church in Grenagh is called St. Lachteen’s. Some references give the name of the church as St. Laghteen. This is a very old Catholic Church. According to the National Inventory of Architectural Heritage/Buildings of Ireland website, the church of “St Laghteen’s” was built circa 1820, and so may be the church where John Herlihy was baptized. For a description and slide show of the church, go to the Buildings of Ireland link at: https://is.gd/NH46ku
To see the location of the church in Grenagh, go to the Buildings of Ireland map at: https://webgis.buildingsofireland.ie/HistoricEnvironment/?REG_NO=20905106
For a Google Street View of the Church, go to: https://is.gd/Um1Q0G
Earlier, on a Google Map you saw the locations of Grenagh, Garryadeen, and Mourneabbey. The map shows that Garryadeen is much closer to Grenagh than to Mourneabbey, and so it is likely that the church in Grenagh was the church that John Herlihy and his family attended. Because St. Laghteen’s predate John’s birth, it is possible that he was baptized there in 1826.
You can view the “R.C. Chapel” in South Grenagh on an Ordnance Survey Map from the 1837 to 1842 time period at the GeoHive website link: https://bit.ly/2WfLTLp
For an ordnance Survey Map of Garryadeen from the same time period, go to the GeoHive link at: https://bit.ly/2Lb2MR2
To read about the parish of Grenaugh/Grenagh published in the 1837 edition of Lewis’s Topographical Dictionary of Ireland, go to the Library Ireland website link at: https://www.libraryireland.com/topog/G/Grenaugh-Barretts-Cork.php