Thank you for all the suggestions. I actually included everything I know about this family, which is almost nothing, in my original post. It's what was in the marriage record for Bridget Loughnane to Jean Hebert. I have not been able to narrow them down to a parish church, just the townland of Cabragh, Fertiana, Thurles.
I have looked at church records for Cashel and Emly and found no Loughnanes or McGraths with the right first names nor any in the townland of Cabragh. I have not been able to find anything in the NLI nor tithe applotments. Griffiths Valuation is too late, although I've searched for others with that surname without finding anything helpful.
There are no arrival records in Canada for that time period and the only church records I found here were for Bridget's marriage to Jean Hebert, the birth of their son, and then Bridget's death the following year. No trace of parents or siblings anywhere under any variation of the surname.
Their arrival in Canada pre-dated censuses and I've tried all the possible variations on the name Loughnane that I could come up with - to no avail. They were RC so I have not looked at Protestant records. Bridget's birth is estimated as 1813 with no emigration date and It's so early in the 19th century I haven't found anything yet.
I have paid for records on the IFHF site but none were the right folks. I'll check out the Irish Times.
I will in future indicate where I've already searched. Thank you again.
Ann