My Powell 1979 "New Zealand Mollusca" includes C.lischkeanus (as
C.kermadecensis), with a mention of C.marmoreus and C.?raoulensis. No
mention of the Auckland live specimens.

However I have just noticed a forgotten annotation at the bottom of the
page, listing records of NZ Conus! I tracked this back to my copy of Bruce
Marshall's 181 paper "New records of Conidae (Mollusca: Gastropoda) from
the New Zealand region", NZ Jour Zoo  Vol 8: 493-501:

howelli Iredale 1929    Wanganella Bank (S Norfolk Ridge), Bay of Plenty 64-228m
raoulensis Powell 1958  Norfolk I, Kermadec Is, Wanganella Bank 44-146m
smirna Bartsch & Rehder 1943    Kermadecs, Wanganella Bank 200-1180m
teramachii (Kuroda 1901)        Kermadecs, Wanganella Bank 300-823m
kermadecensis Iredale 1912      Kermadecs, northern North Island 0-73m

Elsewhere I have seen records of:
flavidus Lamarck 1810   White I, Bay of Plenty, scuba, H & M Seeley 1983
marmoreus Linne 1758    live, Auckland, intertidal; live,
                        Farewell Spit, NW South Island
plinthis Richard & Moolenbeek 1988

Andrew G