If you want something simple to try, use a couple of relays powered from where the motor connects to at the moment: -
EDIT - My knowledge of RC cars is a bit limited to toys that are either full speed ahead or full speed reverse and it has been pointed out that if the car is a little more sophisticated it will control the voltage to the motor so that a range of speeds can be produced. This means that the relay idea will only work on simpler cars of the type that I'm more used to.
A and B are the connections to where your motor is at the moment. Depending on the polarity of A and B, either the left relay closes or the right relay closes. This is set by the diodes in series with the relay coils. The diodes across the relay coils are there to protect the circuitry that feeds A and B.
Without any relays being activated i.e. A and B both inactive, the motor doesn't get fed the 9V. If either relay operates the motor gets fed 9V left to right or 9V right to left. The action of swapping active relay reverses the motor as per a semiconductor H bridge.
Your relay coils need to be rated accordingly to what voltage your current system uses so try measuring this with a meter with a 100 ohm load to simulate the relay in place. Then choose a relay who's coil will work at this voltage.
BTW the relay contacts need to be rated to switch the motor current and they also need to be rated at at least 24V dc switching. To prolong relay contact like fit a 100nF capacitor across the motor.
This will give you an insight into how the H bridge works and if you want to go straight for the semiconductor version then good luck but take advise on ones you think may be suitable.
As for powering the receiver from 9V you ought to use a regulator like a Low Drop Out (LDO) version of the LM7805. This regulator circuit needs to go between the car on-off switch and the circuitry - don't put it before the switch (on the battery side) because after a day your battery will be discharged.