Disclaimer
Modifying your RCX as outlined below WILL void any warranty that you might have with Lego. Proceed at your own risk. You should only attempt to perform these modifications if you feel confident that you're not going to screw things up, and also be prepared to make your RCX completely non-functional.

Here's a picture of the modified RCX with a 9v battery installed. The circled - in the the top right (front of the RCX with the infrared detector) and the circled + in the bottom left are the ones that connect to the microprocessor board.

You can see two 3 pin jumpers, labelled + and -. These jumpers are positioned so that they're between the AA cells. When both jumpers are installed then 9v batteries can be used. When both jumpers are removed, then 6 AA cells can be used. Bigger...

Here's the same view, but with the batteries removed. I marked a + and - just above the 9v battery spots so I can tell which way the 9v batteries are supposed to be installed. The electrical tape is to ensure that 9v batteries with metal cases don't short things out.

I had to cut holes in the green plastic in order to get the 9v batteries to fit. I was able to leave enough plastic at the top and bottom so that the AA cells don't "fall in". Bigger...

Here's a picture showing the wires which were added on the backside. The red wires are positive and the black wires are negative. The + and - written on the metal conductors are how the 9v batteries will be when they're connected. The wires need to be very carefully positioned so that they don't interfere with the surface mount chips and other discrete components on the CPU board. Bigger...

I took a picture of the backside, mirrored it, and superimposed it on a picture of the CPU board so you can see the wire routing. the 3 chips in the bottom right are too high to have wire go over them. Similarly, the three diodes on the left (one is just below the bend in the red wire) are too thick to have a wire go over them. I had to trim back the 3 pin header for negative side so it wouldn't interfere with IC in the top middle. Bigger...

I also took a picture of the bottom portion of the battery case, since I had to remove some if the protrusions here in order to get the case to close nicely. Bigger...