I have identified his wife, Mary Atkins, and his daughter, Mary Burn(s) (or whatever), born about 1815 and on the 1825 and 1828 musters.
Mary appears to have married William Marsh (1832, Castlereagh) but another William Marsh married Mary Ann Bryan (1835 Bungonia).
There are two sons, James (1832) & William (1834) who look secure. But there's a baby born in Cobbitty in 1837 (Mary Ann Elizabeth Marsh) who then goes on to marry in Bungonia so I haven't sorted out whose child she is.
I have identified a descendant of William (1834) who has an Ancestry tree and have messaged him.