J&M is correct. No second time Working Holiday Visas, even on a different passport. see below.(from INZ manual)
WI2.1.1 General conditions
a.The objective of working holiday schemes is to allow young citizens of approved countries, whose primary intention is to holiday in New Zealand, to undertake employment and study during their stay in accordance with their scheme.
b.To be eligible for a work visa under these schemes, applicants, in addition to meeting the requirements of the particular scheme they are applying under, must:i.hold a valid passport from the country whose scheme they are applying under; and
ii.be aged no less than 18 years of age and no more than 30 years of age, unless their scheme allows a different age limit; and
iii.not be accompanied by children; and
iv.meet onward travel requirements (see W2.20); and
v.submit an application in the prescribed manner (see E4.50); and
vi.pay the appropriate fee (if any); and
vii.meet health and character requirements as set out at A4 and A5; and
viii.be the holder of a valid temporary visa if applying from within New Zealand; and
ix
.not previously have been approved a visa under a working holiday scheme, except where their scheme allows a second application (see WI2.20(e) and WI2.160(f)).