Google up OOK (on-off keying) radios. I am using them to report sensor readings back to a main base station. Plenty of them available on EBay. The transmitters transmit when you pull one of their inputs high: they just transmit a sine wave. Likewise, when the receiver senses a signal at the right frequency, it sets an output pin high. Also, they're very small and cheap.
But you are responsible entirely for your own communications protocol and modulation format. In my case, I have each sensor send a series of pulses, each of a length representing the data carried (sensor ID, message type, etc.) , separated by 30 ms. low. I also use a 30 ms. leadin pulse to wake up the receiver, and I use a check pulse at the end, which is a sum of some of the data sent. That is very valuable for rejecting bogus receipts. For a detection scheme, I just run a 2Khz clock, and keep looking for 30 ms. continuous high on the chosen input pin. When I find it, I keep track of the intervals for which the input pin is high and low, and derive my data from that.
One difficulty you might have would be to assure that you don't have the transmissions overlapping. If you had some sort of clocks in your race cars, you could probably schedule transmissions to not overlap.
Good luck
John Doner