American Airlines has round-trip flights from Austin (AUS) to Kailua-Kona, Hawaii (KOA) for $281 with a connection. Flights April to May. Departures on Tuesday and Wednesday. Origin/Destination reversible.
Most of these will require 6-or-7-day stays due to the limited days this departs on.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.