My Great Grandmother was Eliza Brannon/Branney, born 1881. She married Thomas Miller and later migrated to Australia. I haven't got back very far on the Convery side, I'm afraid. Sarah's father was Thomas, born abt. 1822 in Derry, and his father was Andrew. I haven't had any luck with Irish records at all. Trying to research from Australia makes it all the more difficult I think.
Sarah's mother Eliza Doran was born abt. 1822 (baptised 13 Jan 1822) Kirk German, Isle of Man. Her parents were Patrick Doran and Margaret Cain.