However, upon further reflection:
You could use the doorbell transformer and the doorbell buttons to close a two-pole relay. Each pole of the relay would be wired like a push-button per the instructions, complete with its own diode across its terminals. This way the two chime units would not be wired together as each would be switched on separately. They can have a common power supply; it's the common
button that doesn't work.
Now the challenge is to find a relay that works at 16VDC. It might be easy but that's an unusual AC voltage for anything but doorbells. If the relay coil requires a small enough current that the transformer can close it as well as run both chimes, you're in business. Perhaps a 12VDC relay might work, or it might chatter like a buzzer. If you can't find a 16VAC relay you'll have to try this.
If you can't find a relay that doesn't chatter, you could convert the 16VAC to DC; regulate it to 12VDC, and have a good supply for a 12V relay. I'm now going off the deep end: once you have DC, you could have the doorbell buttons turn on a transistor to trip that relay. You could even have the buttons start a 555 timer that would close the relay for a short period of time, starting the cycle for both chimes. This now brings us to the ultimate---
First, a question about how these work: If you don't use the diode on the chime unit, and you hold down the button, does the chime play as long as you hold down the button? If so, make a system that emulates holding down the button for X amount of time. Simply wire the two chimes in parallel, using a relay to close the buttons, not using the diodes, powering the chimes with AC per the instructions; also convert the 16VAC to 12VDC and have the buttons initiate a 555 set up as a one-shot to keep the relay closed long enough for a complete tune to play.
Are these chimes near enough to one another that you hear them both at any locations? If so, they'll drive the client nuts because sooner or later they won't play the same thing or be totally in sync. Now, if you can wire the chimes to multiple locations, you have wires between the units that could instead parallel off of one chime's speaker; get a small Radio Shack amp powered by DC derived from the 16VAC, and use the existing wire to put an additional speaker in the second location where you're trying to get a chime to work.
For an amp, you could use this. It's made to work off a nine volt battery and you could easily make that regulated voltage be 9 volts with the proper voltage regulator IC:
Or even this, if you hate the client (it could happen!):
Edit: just to cover my bases here, I have tried to provide the simplest solutions I can come up with; the most elegant; and at least one using active electronics. Something of this should work for you.
I apologize for using the word "simply," as I believe once people use that word, a lot of details are usually left out. So I left them out.
Last edited by Ernie Gilman on September 18, 2013 12:33.