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www.irishgenealogy.ie is a free Irish government site which has church records for Dublin city. I only saw one record which might be for your family. I also looked for a baptismal record for the father and there are a couple in the 1810-1820 period.
Area - DUBLIN (RC) , Parish/Church/Congregation - ST. ANDREW
Baptism of EDWARD SAMUEL HUGHES of N/R on N/R N/R 1842
NameEDWARD SAMUEL HUGHESDate of BirthN/R N/R N/RAddressN/RFatherJOSEPH HUGHESMotherMARY
Further details in the record
Sponsor 1EMILIA CROLLYSponsor 2ALBERT LAWLESS