In English one can use nouns as adjectives in a role called adjectival nouns, which is great when there are no adjectives to use. However, it does stop adjectives from appearing. Even awesome ones.
New Zealand is a country (proper noun) without a real adjective (apart from the slag kiwi) making the noun the only option (New Zealand lamb), which does cause any ambiguity given the fact that nobody really knows the location of the original Zealand, so no numskull is going to think that new Zealand lamb is a new lamb from Zealand.
However, it should have one. It has one in Italian (neozelandese), where they also convert the new (nuova) bit into a fancy schmancy neo- prefix and they did not even colonise the place.
Okay, I'll have to ignore the horrific Greek/Latin suffix in Icelandic which is a counter-argument for having an adjective for NZ. But I want one and outlandish as it first sounds, the adjective should be New-Zealandish as land is of Old English origin, like the suffix -ish (and landish was actually an adjective meaning native).
Furthermore there is nothing new in new-zealandish as the adjective exists in German (Neuseeländisch), so there is no reason not to use new-zealandish apart from the fact, I suppose, the incredulous stares one would receive would be really bad...
