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Civil registration of births started in Ireland in 1864. Prior to 1864, we only have available baptismal records as a source. Do you have any info regarding Patricio's parents names? I took a quick look at the subscription site Roots Ireland and there were 17 Patrick Torpey/Tarpey baptismal records from 1847-1857. None of the records were in Co. Sligo. Most of them were in Mayo, Roscommon and Limerick. There are also a number of RC parishes which do not have records back to 1857.
So knowing his parents names will allow us to see if a baptismal record is available.