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Here is a link to the RC parish register from 1828-1880 https://registers.nli.ie/parishes/0051 These records are on the subscription site Roots Ireland but when I search for Terence, I don't find a record. All of the nearby RC parishes have records starting before 1840. Roots Ireland also has the Fermoy Church of Ireland records back to 1822. I also expanded the search beyond Cork to the rest of Ireland with no success. I did find an 1829 baptismal record for a Matthew Butler with the correct parents.
Area - CORK & ROSS (RC) , Parish/Church/Congregation - SCHULL WEST
Baptism of MATHEW BUTLER of N/R on 6 December 1829
NameMATHEW BUTLERDate of BirthN/R N/R N/RAddressN/RFatherJOHN BUTLERMotherCATHE LEARY
Sponsor 1TIM LUCEYSponsor 2ELLEN EVANS