Switching between transmit and receive in a transceiver
Assuming you want the two transceivers to "detect" each other, then it is important that you use some sort of random timing for the transmit and receive periods of each transceiver, so they don't get into a condition where they are both always transmitting and always receiving at the same time.

So you are going to want to use a simple microcontroller.  I'm mostly a PIC person, so I'm going to first recommend either the PIC16F1824 or PIC12F1571. Both have internal oscillators so you don't need to add a crystal; just need a source of power and a decoupling capacitor.  The PIC16F1824 is available in the UK from Farnell in a hobbyist-friendly 14-pin DIP package for £1.20, and the PIC12F1571 is available from Farnell in an 8-pin DIP package for £0.52. The PIC12F1571 uses very little power, only 700µA running at 4 MHz.

If you want a UART, for example to be able to easily send characters back and forth between the two microcontrollers, but still need a low cost device, then choose the PIC12F1572 instead of the PIC12F1571.  The PIC12F1572 costs only £0.07 more than the PIC12F1571.

The gotcha with any of these microcontrollers, is that you need an ICSP (in circuit serial programmer) to download the program to your chip.  In the case of the two PICs, the cheapest compatible one is the PICkit 3, which costs £30.71 from Farnell.

Since the ICSP requires three wires (reset, clock and data) in addition to Vcc and ground, this leaves only three GPIO pins free on the 8-pin PIC12F1571 device.  However it is fairly easy to share the clock and data leads with other I/O, so you can really get five GPIO pins out of the eight total.

Besides the two PICs, another option is to use the ATmega328, which is only available in a much larger (28-pin DIP) package for £1.97 from Farnell. It also has an internal oscillator.  You can get a programmer for the ATmega328 from Amazon.co.uk for £16.16.

The randomization doesn't have to be too complicated; for example if you chose to turn each transmitter on for a random period between 200 ms and 600 ms, and each receiver on the same random period, you might get something like this:

transceiver 1: T T T R R R R T T T T T T R R R R T T T R R R R R

transceiver 2: T T R R R R T T T R R R R T T T R R R T T T T R R

                   x       y     x x x x y y y   x x   y y y


Each column represents a 100 ms slice, and the x's show where transceiver 1 is transmitting to transceiver 2 (top line T, bottom line R), and the y's show where where transceiver 2 is transmitting to transceiver 1 (just the opposite).  As one can see, the synchronization happens pretty quick, often within a second.

I coded this algorithm up in Python and did a Monte Carlo simulation of it (10,000 runs), and the maximum time it took for one transceiver to lock into the other for a minimum of 100 ms was around 2 1/2 seconds.  If one sets the minimum transmit/receive time to 200 ms, then the maximum lock-in period rises to around four seconds; at 400 ms it can take eight seconds.

Once the two devices have synchronized together, you can then have them talk back and forth in an alternating fashion using fixed transmit/receive times.

transceiver 1: T T T R R R R T R T R T R T R T R T R T R T R T R

transceiver 2: T T R R R R T R T R T R T R T R T R T R T R T R T

                   x       y


Note after the second transceiver has been synchronized (at y), from then on the two transceivers can swap transmit and receive roles back and forth every 100 ms.  However since the internal oscillator on the PIC12F1571 has a maximum tolerance of ±2%, the two transceivers could drift 4% apart, or 4 ms every 100 ms.  This internal oscillator error can be corrected by modifying a register, so the two oscillators could be brought very close together, but this must be accounted for.

To turn the transmitter and receiver on and off, you can use a low-side switch:



where "load" represents either the transmitter or receiver module (so you would need two of these). The N-channel FET has a low V\$_{GS}\$ (1.0v) so it can be driven directly by the microcontroller's output.  The FET is also available at Farnell for £0.52.

You can use other pins of the microcontroller to handle input/output of the transmitter/receiver, and to generate an output when the transceivers have synced.