Here's a possible birth record from www.irishgenealogy.ie/ (free site)
Area - CORK & ROSS (RC) , Parish/Church/Congregation - DESERTSERGES
Baptism of BETTY MURRY of N/R on 15 June 1844
NameBETTY MURRYDate of BirthN/R N/R N/RAddressN/RFatherPAT MURRYMotherNELL MCCARTHY
Sponsor 1PETER MAHONYSponsor 2MARY CARTHYRecorded Parochial AreaDESERTSERGES
Book NumberPageEntry NumberRecord_IdentifierImage FilenameN/RN/RN/RCR-RC-BA-127023cork & ross.desertserges.p4798.00439
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If this is correct you or I can search for the parents' marriage record