stepping down 12c AC to 6v AC in small space

I don't have the room to put a transformer in since space is small and need to drop 12vac to 6vac in a safe way (this will be on top of a christmas tree). I did some research and seems zener diodes are the way to go, however I am not sure how this would work with AC, how to connect them or even what ratings to look for. Any help would be greatly appreciated, thanks!

What are the power or current requirements? If the load is constant a resistor might be
enough.

MarkT:
What are the power or current requirements? If the load is constant a resistor might be
enough.

here is what I am powering Dropbox - Error
its a motor, and behind it I have a rectifier so I can run 2 LEDs. There used to be a lightbulb but it burned out, and I am assuming that dropped the voltage roughly 6v, so I have to compensate for it else the motor gets very hot.

problem with resistors is I would need something like a 5w+ resistor which I have only seen HUGE version of, maybe I am missing something? Those are a bit big for what I need.

Hmm, tricky, induction motors are very inductive. Yes a power resistor would be
bulky since it needs to dissipate the heat. A transformer is still the obvious solution...

MarkT:
Hmm, tricky, induction motors are very inductive. Yes a power resistor would be
bulky since it needs to dissipate the heat. A transformer is still the obvious solution...

are there transformers that can fit in that small of an area? I have about 1/2inch to fit components

An unpolarized capacitor matched to your current draw will do the trick.
The formula escapes me but there's something equivalent to the DC V=IR for RC circuits. If you can't find the formula I'd start with 100nF, and measure the voltage across the motor. Depending on the voltage, try a bigger or smaller capacitor.

Yes half an inch square is enough for a transformer.