I found this circuit of a 12V to 9V converter.
There is little to be said about this circuit. All the work is done by the regulator. The 78S09 can deliver up to 2 amps continuous output whilst maintaining a low noise and very well regulated supply.
The circuit will work without the extra components, but for reverse polarity protection a 1N5400 diode is provided at the input, extra smoothing being provided by C1. The output stage includes C2 for extra filtering, if powering a logic circuit than a 100nF capacitor is also desirable to remove any high frequency switching noise.