Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Singapore to Haiti as you normally would.
Singapore Changi Airport is SIN and Port Au Prince Mais Gate Airport is PAP. These codes are created by the International Air Transport Association (IATA) and airlines use them to identify the departing and arrival airports in the flight routes they service. Cap Haitien Airport (CAP) are other airports near this flight route and their unique identifiers/IATA codes.