I recommend that you pass level 15 of the Beach Patrol side mission to get infinite swimming stamina and that you take over most of the empires so the gangs won't bother you before you attempt to get these cars.
Many players know that you can get the Stinger simply by shooting the driver in the head and quickly getting in the car while he is waiting at the start line, but I don't know of anyone who have found a way to get the Infernus and Cheetah in their FP/TP form before now.
Mission: Turismo races
If you want the Stinger, select race number 4.
For Infernus, select number 2 or 9.
For Cheetah, number 6.
Choose a race and find a strong vehicle, for example a fire truck. Drive over to the starting marker but don't enter it.
Get a good speed and aim for the racing car you want and bail out of your vehicle just before you hit it. What you want to do is to hit the racing car so hard that it will flip over and land upside down. The race will start if you don't bail out and you don't want that to happen.
When the racing car is upside down it is much easier to push but you still can't push it to hard or you will trigger the race.
Push the car over to some shallow water and flip it over again. Push it all the way into the water. For some reason the driver won't drown so you have to kill him. Select a gun and shoot him in the head. The screen will fade out and you will fail the mission but the car will still be there with its door open. Push it out of the water and don't let its door close before it is in your garage.
I did this on PS2.
(Sorry for my bad english)