Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Honolulu to Port Moresby as you normally would.
Leaving on a Monday is a viable option for saving on travel. Heavily demanded days of the week can typically drive up the prices you see. Booking your travel for a less competitive day can save up to 39% on the overall cost on flights from Honolulu to Port Moresby.