My pleasure !!
First have you tried an Invercargill Cemetery Search? Check this :-http://www.icc.govt.nz/ServicesA-Z/Cemeteries/CemeterySearch...
Looks like I found all of them .. perhaps !!
Also the NZSG Burial Locator ( I have a copy) would be worthwhile. I also can acess the microfilm records for the Southland Times and published death / birth notices at the Invercargill City library.
Have you tried BDM .. Birth Death and Marriages NZ, Historical records. This should in most cases disclose births and deaths or even marriages.
Hope this helps. If not get back to me. Can e mail direct if you want.