I have an image stabilization camera, the Panasonic Lumix. I strongly recommend it, not just for people with shaky hands, but for everyone! The Canon cameras marked "IS" have it. The Kodak doesn't, I think.
With the Panasonic, you can literally jump up and down while shooting and still get a clear image. The only way it doesn't work is with a long optical zoom.
So I can recommend adding any of the Lumix family. The one I have is the DMC-FZ7. It is not the most compact camera in the family, but does have 10x optical zoom. Not everyone really needs that kind of zoom, and I think 3-4x is a long enough zoom for practical purposes.
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