They started minting back in 2004. I have them all except the first two year (they are very expensive; $300 to $400 USD). http://worldsilverbullion.weebly.com/kiwi.html
The earliest bu I can find is 2006 with 3000 minted. I believe it might be pretty expensive to put this set together. Proof kiwis started abit earlier
Oops, missed 2 years. Recent TradeMe auction for the 2004, $325- https://touch.trademe.co.nz/listing/view/879280948 http://forums.silverstackers.com/message-345004.html
Good to hear your interested in these coins A great series to start collecting as they were minted in BU with the carded version and proof as well House is correct the 2004 - 05 and 2006 are the least minted and most expensive The Icon series is 2009 - 2011 followed by the treasures 2012 - 2014 The latest release ja a glow in the dark kiwi and quite appropriate as that's when they come out to feed Drop me an email or PM if I can assist you with collecting these as I have a few of them