Hi, the information you are looking for does not seem to exist in the records of the Church, the baptism records dating back to 1802 have been transcribed for the Roots Ireland site, there appears to be only one Carey baptism recorded :
Henry Cary 1843, fathers name Thomas
There is also only one Carey marriage recorded, Elizabeth Carey, 1828, who married a James ?
Sorry also now see Margaret's marriage to William Riddles, but her fathers name is not given in record (Or was not recorded in transcription)
I can only see one Margaret Carey baptised in the larger Derry area who could have conceivably been William Riddles bride although she would have only been 16 in 1832,
Margaret Jane Carey baptised 1816 St. Columb's Cathedral, father George Carey, mother Cathirne
Regards
Joe