rabbit9, you might be hearing "water hammer". This occurs when the flow of water is suddenly stopped/reduced or has its direction suddenly changed. I am not sure of the following; I believe that the device reduces the flow of water rather than the pressure. Maybe it reduces both (it has been a long time since I had to visit Boyle's law). I would try and slow down (damp) the activation of the pressure regulator or reduce the input of the water by installing a gate valve ahead of the regulator. I get some serious pressure off a reclaimed water supply. To use a hose effectively, I attached a shutoff valve first and then attached the 'trigger'. I adjust flow, pressure (and recoil!) by stopping down the shutoff valve and thus I can water seedlings and also blast aphids off the hedge plants without much fuss.

Excellent suggestion. Thanks!

BTW, it isn't a one-time pulse, as one might expect with water hammer (a big WHAM! when you turn on or turn off the water). It is continuous pulsing that will go for as long as I leave the water turned on. My guess is that it has something to do with the water velocity and the length/diameter of the pipe, a bit like a pipe organ if you know what I mean. Anyway, I'm betting your idea of changing the water flow with a gate valve should stop the resonance. At least it's relatively cheap to try it.

I fixed the zone that was pulsing this way.

First turn on the pulsing Zone! Unscrew the Solenoid on the valve about a 1/4 (or less) or just enough to see the zone kick on. If a small leak develops unscrew the solenoid and use some Teflon tape on the threads of the solenoid to stop the leak. Be careful not to loose the small rod and spring when removing the solenoid. Clean the part before you reinstall them. Then do the 1/4 "back off" turn trick again. This fix may or may not work for you, it depends on the problem you have.