The interactive map states that there are officially no drop boxes by the terminals. However, the interactive map says there’s a dropbox prior to the airport on Pao’o Street, across from the car rental locations.
I was able to find it with Google Maps:
The drop box is in the little loop in the lava/dirt on Pao’o Street south of Keahole Airport Road. If you’re driving into the airport, you’ll turn left on Pao’o Street and it’ll be immediately on your left.
Last updated 10 June 2017