No car rental places at the port. However, Avis and Alamo both had shuttle buses picking up passengers at the port and shuttling them over to their locations. That's what we did when we got off the ship--took the Alamo shuttle to their location near the airport and got our rental for the day.
All the majors have shuttles to their airport locations. However that takes some time. There are a couple with outlets close to the port.
We used Enterprise, which has a spot about 5 minutes from the pier, and that worked out well. Think Budget has one in the Hyatt Hotel close by as well.