Tiffany, I just looked at Peter Pan bus schedule and it doesn't look like they run busses to Newport that late at night. You are really between a rock and a hard place. I would say to you to book a hotel for that night and leave the next day for Newport.
I would call some of the major car rental agencies and ask what the age for car rental is. You may find a couple that will do a rental under 21.
The problem w/ arriving Green that late in the evening is that everything pretty much shuts down at the airport. You could find a taxi to bring you to a hotel or perhaps a free shuttle. There are hotels right there at the airport also.
We just flew into Green from San Diego in March and the airport was virtually dead! There are not that many flights arriving at that time of night.
However, where there is a will there is a way! You are about 40 min. drive to Newport from Green. We just drove to Newport for the day this past Sunday and we were 45 min. away.
If you are visiting someone could they pick you up at the airport?
If you are traveling alone, I would be leary of taking a cab by myself at that time of night, not to be doom and gloom, just cautious. Can you fly in on an earlier flight? I am just giving you suggestions in hopes that you can find a solution.
Let us know how you are making out. We will try to help you get to Newport.