(Catholic) Carey Family from Donegal

I am searching for leads to the Irish ancestors of Frank Carey, (probably Francis Joseph Carey), believed to have been born in Donegal around 1856.  He emigrated to the US with his mother, Bridget, from Liverpool England, about 1864

The following information is based on information found on a Death Certificate recorded in the US:

Name: Frank Carey

Place of Birth: Donegal, Ireland

Father's Name: John Carey

Mother's Name: Bridget Dunlevy (but possibly Bridget Dever.  US family records of several siblings of Frank list their place of birth simply as Ireland, and their mother's name as Bridget Dever, not Dunlevy). 

Further unsubstantiated information:  Bridget's father is assumed to have been named Edward Dunlevy or Dever.  Her mother is believed to be Margaret Kennedy, married name Margaret Dunlevy or Dever.

There is no documented information of where Frank's father, John Carey, was from in Ireland.  The family is Catholic.  I have used the rootsierland.ie search engine and other search engines extensively to find any records for the family in Donegal, and have been unsuccessful so far.

YDNA testing has found that my Keary family of E. Galway is related through sharing a common male ancestor with this Carey family, most probably more than 300 years ago.

Thanks so much!