Basic RF ping-power transceiver for 100s of nodes
If you insist on using RF, you might get some joy from super-regenerative receiver circuits. These normally pulse at supersonic frequencies. Circuit time constants could be slowed to pulse-per-second.

Very simple circuit having just a few transistors

Low power drain from a few battery cell

Super-regen circuits are both transmitter and receiver combined.

Range possible: tens-of-meters (a guess)


Super regenerative receivers are notorious for causing interference with one another when their RF is tuned to the same frequency. This is exactly the action that you are after. You may be able to get them to self-sync, or at least affect one another.
Getting a super-regen to pulse its RF at one or two second intervals may be difficult. It is possible to build a super-regen around a tiny microcontroller. The timing functions of any microcontroller would be used to delay the RF sync pulse. The microcontroller could also sense pulses from other super-regens. See: http://www.eix.co.uk/Articles/Radio/Welcome.htm
 Dr. Eddie Insam includes a super-regen externally-quenched microcontroller circuit idea, among others: