For what I could find of information here and differend places (small semiindependent nation, with little informtion), Cook Islands needs the following two issuing entities:
Goverment
Wikidata: N/A
Example: N#303167
Ministry of Finance
Wikidata: N/A
Example: N#202754
Hope it's usefull, thanks :D
Sources:
https://en.wikipedia.org/wiki/Category:Finance_ministers_of_the_Cook_Islands
https://www.moneypedia.de/index.php/Signatur:_Cook-Inseln
https://en.wikipedia.org/wiki/Cook_Islands_dollar