If the volt meter uses a constant 30mA at 12V, then it could be modeled as a resistive load. The load would look like 12V/0.03A= 400Ω
You could then find the RC time constant: a 100uF capacitor and the 400Ω load would take 0.04 seconds to drop to 63% of 12V or roughly 4V.
The problem with using a capacitor to smooth out the voltage is it will immediately drop, if the voltmeter requires a constant voltage (within a certain tolerance like ±0.3V) then a very large capacitor would be required. This leads to large inrush currents and problems with the rectifier.
A better way would be to use a voltage rail higher than 12V and voltage regulator with a capacitor to regulate to 12V. Keep in mind that with realistic values for capacitors it will be difficult (not impossible) to design a circuit to maintain voltage for more than ~1 second at 30mA. Batteries are also a great way to provide energy.