Note: This can only be done while playing on Xbox Live:
Step 1: While in an Xbox Live room choose the car that you want to have a new color. For example, the Porsche 911 GT1 is only available in one color (white). If you want to make it a different color, choose that as your car.
Step 2: You must now select the color that you want to change it to from another car in a different car class. For example, if you want the Porsche 911 GT1 to be pink, while still in the Xbox Live room choose the Classics car class, then the Mercedes 300SL Gullwing and select it in pink.
Step:3: Exit out of the Xbox Live room, but do not sign off Xbox Live. Then, back out all way to the single player mode, go to "Time Attack", then to "Car Challenge". Select the same car as you did the first time. For example, the Porsche 911 GT1. When you pick that car, you will be asked to choose a transmission type. Do not choose either of them; instead press Back until you reach the single player screen.
Step 4: Go into an Xbox Live room. You can either search for one, create one, or return to where you originally started by quick joining your buddies game. This glitch is probably most useful during games such as Cat and Mouse.
Note: You can only change it while you play online. If you go to change the car that you had just changed the color of, the color will get reset. You must take the color that you want from a different car class. This does not change the speed of your car.