I've hand-sketched the simple cct of variable linear regulator that will fit the bill - please excuse the quality of the drawing...
Note that the efficiency of such regulator is going to be less than 30%, so it will drain your 9V battery fairly quickly.
If you want the more complicated solution, like say DC/DC converter, in order to increase the efficiency, please indicate that here.
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Addition: Just realised looking at my cct that, if the current drawn by the load is ~100mA, then the transistor power dissipation is going to be just under 1W, so BC547 may not be up to the task... in which case, use any NPN bipolar transistor rated appropriately (just ask the sales guys at Dick Smith or Jaycar, or wherever you will shop), and MOUNT it on the heatsink.
BC547 should be OK if the current consumption is limited to about 40 mA.
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