I'm looking for a new digital camera to replace my trusty Sony Cybershot. Problem is, I have a condition that gives me shaky hands... not bad, but it makes about 50% of the pictures I take under low light worthless. Does anyone have a suggestion of a nice small 10MP or so casual digital camera with good stabilization?

If you don't need to blow your images up very big or do much cropping you really don't need 10MP. I won't make any difference.

agreed, there's absolutely no need for 10MP if you're an average joe.
The MP craze is mostly a marketing strategy. They put the big numbers in there for how it looks on paper so don't get fooled.
Sometimes you'll find that camera's with big MP's have crappy sensors that produce VERY bad images. (lots of noise for example)
If you enjoyed using your sony in the past, you should continue using them now coz they're still very good performers.
They usually produce nice and sharp images with good saturation (although some may think it's over saturated).
Stabilization wise, I have no idea as i can't remember. But you should just do a google on it.
Canon IXUS's are always popular too. And for good reasons.