I believe the problem is that as forces of nature go, gravity is exceptionally weak. Consider how much difference there is between someone on Earth, and someone just a hundred diameters away, and thats they gravity created by something as big as the Earth. Meanwhile an electromagnetic signal can travel for a very long distance even at very low power.
A good point, but still, I try not to underestimate sciences ability to take advantage of something that seems hugely improbably rather than out and out impossible...
Kirk, the effect you describe (moving a mass around and detecting the effect) is what I understand scientists are searching for with a thing called LIGO (Laser Interferometer Gravitational-Wave Observatory), which is kilometers in size and exquisitely sensitive. But like Eric said, gravity is just way too weak. Two years ago, Ray Chiao, a profesor from Berkeley, suggested that superconductors might be able to efficiently convert photons into gravitons (which would have allowed gravity-based communication and who knows what else) but I haven't heard anything since then and assume that the experiment didn't work.
Be sure to check ut the story of the gravity stone:
http://kisrael.com/viewblog/?date=2001.01.23
(I guess Colby had one too: http://septor.name/colby/gravitystone.html )