The Kauai Marriott in Lihue has a good koi population in the waters on their grounds, though I doubt you are looking for that epic 'pacific island carp adventure' not to mention being removed from the premises. I was just there in January and thought about it each time I walked through the hotel.
The waves and sand always take place of fishing when I go to Kauai, but below is a URL that contains some info on trout fishing in a stream on the island. Lots of effort to get there, a multi-day trip, so it probably won't apply in your scenario but is something I hope to look into during future trips there.
http://www...he+Koaie+-+Kauai,+Hawaii
Kauai bash anyone?
I saw quite a few links regarding freshwater options for Kauai, so more applicable info to your inquiry is out there. A few years ago I was on a kayak/hike on some private plantantion land and was a little surprised to see bass in the small creek among the tree roots in the water and swimming around my kayak.
I will add a fly rod to the next trip there. Good luck!