Yes it is sometimes spelt Buninyong and yes I did contact them and no they are absolutely certain that he was not born there or anywhere close by or that there were any Kirker's there at all. So I'm fairly certain that this is a red-herring - though I haven't crossed it off completely.
Death certificate for 1914
Name: William Kirker
Age: 77 (which would put his birth as 1837)
Where born: Bunniygong, Victoria, Australia
How long in New Zealand: 44 years (which meant he came to New Zealand around 1869/1870
Name of father: not known
Name of mother: not known
Profession of father: not known
There is no informant mentioned - just has the name of the medical attendant and when the attendant last saw him.
On his marriage certificate for 1884 he states his age as 35 which would mean he was born c1849 which is 12 years later than his age on his death cert.
On his son Robert Alexander birth cert he states his age as 44 which gives a birth date of c1850 and birthplace is just Victoria.
On one of his other children's birth cert his birth date works out to be c1845 and his birthplace is Belfast, Ireland.
I haven't yet managed to find an immigration record for him to New Zealand so can't confirm when and where he came from with that either.
His marriage certificate is the earliest document and since he gave the information is hopefully the most reliable.
The Australian connection is very confusing as the records for Victoria, Australia BDM's are very good but he's not on any of them and the place he mentions says he could not have been born there as it was not settled during the 1837-1850 time period so there is no way he could have been born there.
I did find this Australian record which might shed some light... or not
"A William Kirker was transported to Australia on the 10 Sept 1846 to NSW - ship "Henry Packer?" sentenced to 12 years - was this man his father?- source the Phoenix Hulk Transportation Entrance Records for 1838-1846 "
and also this Belfast record
"21 Sep 1859 • Belfast
12 year old William Henry Kirker disappeared - his parents were William Kirker and Mary Ann Wilson"
With all the leds to William Kirker hitting a dead end I thought looking at his parents might help (though I know it is not the best way to do things). Hence the query about William KIRKER and Mary BROWN.
Hope this helps