For this purpose, I think your most direct and easy route is to look into On-Off-Keying (OOK) modulation.
You can pickup an off-the-shelf oscillator (digital oscillators are cheap and abundant). Something like 24MHz would work. Have the oscillator go into an AND gate. The other pin is your serial data stream. Logic 0? No transmission. Logic 1? output=frequency. You will need to implement a 5th order passive filter at a minimum to round out the harmonics (72MHz, 120MHz...etc). A simple wire of 3m would work for your antenna. It wouldn't be ideal, but it would work.
The hard part is the receive.
Starting with a similar 3m long wire, you would need to connect it to an LC tank filter. From that, you have a few options. The easiest method possible, is getting a log-amp like the AD8307. That gives you an output proportional to input signal power. No input power? No output. Lots of input power? Max output. It's an RF-to-DC converter (not quite, but close enough). If you can't swing that, the next best bet is to implement a mixer- either a gilbert cell or a diode ring mixer. (All of which are googleable). Use another oscillator of the same frequency to get close to the transmitter frequency. (Ideally you would want a PLL).
Low pass the output of whichever device you choose at about 5x the data rate (so if you are transmitting 300 bps, your low-pass filter will have a cut-off at 1500 bps). If you're using the AD8307, you should be able to get away with a simple comparator to recover the bits (you'll need to check your polarity - that a 1 comes out to be a 1). If you're using the other methods, you'll need some simple amplifiers to gain up the receive signal enough to drive a comparator with some hysteresis. Again you would recover your digital bitstream this route.
Cheers!
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