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Kinneigh is a civil parish and the related RC parishes would be Enniskean/Desertserges (records starting 1813) and Murragh/Templemartin (records starting 1834). Both of these parishes are in the Diocese of Cork and Ross and records for that diocese are on the free site www.irishgenealogy.ie Keep in mind that James Hurley and Mary Donovan would have been very common names and there could be a number of couples with those names in that area of Cork.
I did find a baptismal record for a James Hurley in January 31, 1825 in Enniskeane with those parents. There was also an Anne baptized June 25 1817, Daniel November 1831, Norry May 13, 1831. All were in Enniskeane/Desertserges parish. Obviously, Daniel and Norry were baptized six months apart so they were not brother and sister.
Do you know the names of the children? Obviously John was one son.