No Marriott properties on Kauai offer rooms at the government rate, as far as I can tell. I have tried many times to book a room at this rate while on official business (I believe it is $157/night for Kauai, possibly seasonal) and have never been successful. To contrast this with Oahu, I have never had a problem at the Waikiki Beach Marriott Resort & Spa after no less than nine separate stays with them (with a duration of up to two weeks per stay).

I can't justify the $250+ rates for the most basic rooms on my expense report so I stay at a local condo while on the island.

See this link for an article on an upcoming Courtyard on Kauai, up in the Waipouli Beach/Kapa'a area. Hopefully the rooms will indeed be "moderately-priced" as the article explains.