I have managed to get some recognisable shots through a point and shoot digital camera of Saturn, Jupiter, and of course the moon.
I have used a Canon A40 2Mp camera with my shots. I'm not sure what you can play with with your camera, but when I took my shots I set the camera to the Macro (i.e. close-up) mode, but with everything else set to auto (accept the flash - turned that off, but I usually forget this for the first shot back after a break...must really scare the neighbours peering over the back fence
).
With everything on auto, the camera is left to evaluate the field of view and set the appropriate shutter speed and aperture. The trick I have found is to use the optical zoom of the camera. This means that the planet takes up more room in the field and it is easier for the auto settings to recognise the detail (such as banding on Jupiter). I find that it is easier for me to handhold the planet in the camera field of view. This also removes the field stop of the eyepeice from the shot - something you might see while snapping at the moon. When I don't zoom I seem to get more over exposure of the planet - banding virtually invisible on Jupiter.
I also use an 8mm Radian eyepiece which has long eye relief (and a large eye lens) and this maybe important - it certainly makes it a bit easier.