I just rented an Alamo Mustang convertible in Kauai at the other end of the island chain a couple of hours ago. $26.62/day when you divide the bottom line with all taxes/fees by the 25 day keep. Not many convertibles left on the lot though; just the 1 Mustang I snagged, and 2 Chrysler Sebrings. Has some scratches/dings, but I documented everything so there's no issues when I return the vehicle. About 1/2 the normal rate though ($50+/day all-inclusive is the normal rate for a long keep convertible) so I'm a happy camper.

I did a quick search (Alamo, Hertz, and all majors on Orbitz) and found zero availability for your dates of travel. Four suggestions.
1. Try an independent. Harpers Rental is 4 miles away from the airport and is the only company allowing 4 wheel drive vehicles on Saddle Road and Mauna Kea(rough roads in the center of the island). Best to call them at 1-800-852-9993. Haven't used them myself, but have heard good things about them. There are likely other independents that people overlook.
2. Try an off-airport location. Hertz and other car rental places have some satellite locations at hotels and marinas.
3. Try through the place you are staying at. May be easier for them to find a rental for you, they may have an arrangement with a particular firm that will set aside vehicles for them, and they'll be happy to book it for you because they likely get a commission.
4. If everythings totally booked up, still keep trying until your date of travel, and then check when you get to Hawaii if you still haven't found anything. Invariably there are some no shows, and you might get a walk-up rental.