New York to Los Angeles

I am from Belgium, and me and my son come to visit USA in july this year. We stay a few days in New York an make a trip to

Atlantic City / Washington / Knoxville / Nashville / Memphis / Natchez / New Orleans / Baton Rouge / Houston / San Antonio / New Mexico / Santa Fe / Taos / Grand Canyon / Las Vegas / Palm Springs / and Los Angeles

there we stay with friends. From Los Angeles we fly back to Europe (Brussels)

I would like to do this trip with a mid-range convertible, but at this moment i am having problems to find such a car to rent for this one way trip

Suggestions about my trip or renting-problem are welcom.

greetings from Belgium