The source of my information was the article by Brendan Kiely on 'The/Na Connerys' in the book The Companion to Irish Traditional Music, ed. Fintan Vallely, Cork University Press, 1999.

James, or Séamus, was transported to New South Wales in 1835 on the evidence of the land agent's brother (who was the grandfather of Sir Arthur Conan Doyle). The other two brothers, John (Séan) and Patrick, were tried in Waterford in 1838 where they were sentenced to transportation for fourteen years.

Their lives in Australia turned out well for them with Patrick and James becoming successful contractors in Sydney. John became a Presbyterian and died in 1851, James died in 1857, while Patrick lived on until 1880.

The link I gave above for Brendan Kiely's book on Na Connerys doesn't work any more, but a good search should yield information about the book and its availabilty.

Who the Connerys actually were and what they did is fascinating, but what is even more fascinating is the transformative process which has made their simple story one of the starkest and most powerful accounts of the suffering of the Irish.   

Hope this helps.