I would suggest using either a DC-DC converter with integrated LDO regulator, or using a buck-boost DC-DC converter so that as the power output from the 9V battery drops below the threshold for the step-down component of the converter, it changes to step-up mode. This will give you the best performance and lifetime from the battery. National/Maxim/Linear Technology all do parts which can do this.
If you need the cheapest option, then you probably should look a a low-drop out regulator (LDO) with maybe 200mV dropout voltage. This will give you operation from your input 9V downto 5.2V. However when the input voltage is greater than 5V all the power is dissapated as heat in the device.
alpha