Doesn't help with his parents' names, however - of possible interest, from the NSW BDM index:
Children of John and Jane PIPER (these are probably baptisms rather than birth registrations, as pre 1856):
1842 Elizabeth (Wesleyan Methodist, Sydney)
1844 William (Wesleyan Methodist, Wollongong)
1847 John (Wesleyan Methodist, Wollongong)
1849 Jane (Wesleyan Methodist, Camden)
Children of James and Martha PIPER:
1843 Caroline (C of E, Illawarra, Jervis Bay)
1843 William (C of E, Illawarra, Jervis Bay)
1843 James (C of E, Illawarra, Jervis Bay)
1844 John (Wesleyan Methodist, Wollongong)
1847 Elizabeth (Wesleyan Methodist, Wollongong)
1848 George (Wesleyan Methodist, Wollongong)