Came across this thread on ancestry and thought my search matching your family is long shot, but you never know.
I am searching for a Denis Byrnes who married a Margaret Bumbury, I would take a guess and say in Tipperary.
They must have immigrated to Australia around 1840.
My gg grandmother was Annie Blamey, died 1916 at 77yrs.
Her parents were Denis and Margaret and she was born in Tipperary according to a death transcription I have.
Denis is listed as a candle and soap maker.
At the time of Annies death she was listed as being in New South Wales, Australia for about 70 years.
I am guessing that she came with both her mother and father.
I cannot seem to find any records of where and when they entered Australia.
Look forward to your reply.