Article 47 (Amendments)

1.

Any Party may propose an amendment to this Convention. The text of any such amendment and the reasons therefor shall be communicated to the Secretary-General who shall communicate them to the Parties and to the Council. The Council may decide either: (a) That a conference shall be called in accordance with Article 62, paragraph 4, of the Charter of the United Nations to consider the proposed amendment; or (b) That the Parties shall be asked whether they accept the proposed amendment and also asked to submit to the Council any comments on the proposal.

So here is all that New Zealand needs to do if it is worried about the Single Convention when it wants to legalise the weed beyond the point of allowing people to grow and use a few plants unmolested (something that can obviously be fitted without any difficulty into the existing Convention, as comment 4 makes clear).

Should other Parties not want to buy New Zealand's amendment then there is