Have you exhausted all the avenues at the Australian end? Some convict records can give details of family, or other clues.
I havnt been able to find much and I'm not sure where to look. I was told that they might list parents on burials in Australia.
Someone did find that John was given ticket of leave papers in 1851 which would allow him to move about the county he was in but haven't got anything after that.
Was he sent to Tasmania or NSW? The ship he was sent on appears to have stopped at both places. Find My Past has Tasmanian convict records. Ancestry has NSW records. There may be other places which also hold records.
Yes, depending on dates and places, Australian death certificates can give parent's names. BUT, that depends on whether or not the informant knew their names. Sadly they sometimes don't and sometimes they get it wrong.
Are these the facts for your John? Transported for 10 years in 1847? Departed 8th August 1849 on the ship Adelaide, arrived 29th November, 1849? Given ticket of leave in 1851, two years after arrival? I don't know a lot about convict records, but that doesn't sound quite right. I would be double checking that is the right John Bon*et* getting his ToL in 1851.(there are a couple of other convicts with that name)
Have you asked for assistance with John on the Australia board?