Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Kaua'i to Birmingham, Alabama as you normally would.
In terms of precipitation, rainfall in Birmingham, Alabama ranges from 3.4 - 5.2 inches per month. March is typically the wettest month, when rainfall can reach 5.2 in. October is typically the driest time to visit Birmingham, Alabama when rainfall is around 3.4 in.
If weather is an important factor for your trip to Birmingham, Alabama, use this chart to help with planning. For those seeking warmer temperatures, July is the ideal time of year to visit, when temperatures reach an average of 80.6 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 44.6 F).