Natural light does seem to work best. Flash can alter colors or can glare off shiney parts of the coin and cause uneven lighting of the coin surface. Side lighting with a small flashlight can sometimes help but can also alter colors.
If you want really crisp pictures, buy a compact tripod (about $20 or less) that allows the camera to be tilted straight down so the lens can be completely perpendicular to the surface of the coin, providing an equal focal distance across the entire surface of the coin instead of one edge of the photo being more sharply focused than the other edge. Of course, no matter whether you use a tripod or another type of rest like a can of soup, you have to pay attention so you're not throwing a shadow on the coin or just a portion of the coin. Better the entire coin is in the shadow (as long as it has enough light to show good detail) than partial shadow (the uneven lighting thing again).
Very few people can handhold a camera rocksteady enough to get sharp photos that show detail on small objects like coins, so I really recommend some sort of mechanical camera support.
You'll get the hang of it!