Birth registration only started in Ireland in 1864. Prior to that you have to rely on church baptism records.
Here’s Curry & Martha’s marriage in 1854. Both lived in the townland of Ballylisk, in the parish of Kilmore:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1854/09463/5429170.pdf
Tradition was to marry in the bride’s church (though it might have been the groom’s church too). Mullavilly Church of Ireland has baptism, marriage and burial records from 1821 onwards. There’s a copy in PRONI in Belfast. I don’t think the records are on-line anywhere.
Griffiths Valuation (1863) lists a Thomas McClogher in Ballylisk. Perhaps a relative? He had plot 11f, a weaver/labourer’s cottage. There was also a Curry family in the townland, so perhaps that’s where Curry got his forename. Here’s a death for a Thomas McCloughan nearby in Tandragee, in 1882 aged 66. A brother to Curry perhaps?
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1882/06405/4839469.pdf