Shaun, I have to comment that you have amazed me once again.
Are we now looking for the 'second son' who fits in between James and Daniel? It is so hard to give up on a search when there is a tiny clue to more possible information.
Based on a pittance of clues, I once found the following:-
Arthur J Joyce, Newspaper Writer, London, born 1819, Bath, Somerset. I was never able to find out any more. James Parker Joyce named one son Arthur.
He also had a son called William James, born 1865, not recorded in his obituary.
Papers Past - By 1 May 1863, the Joyce party of gold miners struck it rich at Maori Point on the Shotover River. Each member of the party had 60lbs of gold after six weeks of work. They went back for more!
Michael Joyce
James Joyce
David Finlan
William Ryan
Peter Kelly
Michael Darmaby
Sudden riches. What did they do with it?
Papers Past 1863, James Parker Joyce advertised his Royal Hotel at St John's Kingston.
Michael Joyce, 1816- 95, had a ship built! He was referred to from then as Captain Joyce of Port Chalmers, although he had been in the Water Police in Australia.
I cannot help but connect these incidents. Michaels' son John was born in St Ives in 1839. He became a lawyer and was MP for Lyttelton. Another son, Michael, 1846-1882 lived in Sydenham.
Were the two men brothers, or were they father and son? The New Zealand picture seems to show up a lot of uncle/nephew emigrations also.
This is why I thought originally that the message about The death of James Bailey Joyce was in the Lyttelton Times.