Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Arizona to Port Au Prince as you normally would.
In terms of precipitation, rainfall in Port Au Prince ranges from 1.2 - 8.3 inches per month. May is typically the wettest month, when rainfall can reach 8.3 in. January is typically the driest time to visit Port Au Prince when rainfall is around 1.2 in.
If weather is an important factor for your trip to Port Au Prince, use this chart to help with planning. For those seeking warmer temperatures, June is the ideal time of year to visit, when temperatures reach an average of 86.0 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 80.6 F).