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OK, ice made from heavy water would work, but a MUCH cheaper and easier way is to make ice from a saturated sugar or salt solution. Heavy water will cost you about $1 / mL - if you can find any.
When you dissolve sugar or salt in water, the density increases - the sugar / salt "fits in between" the water molecules, and the volume barely increases. Sugar is easier, because it will freeze in your normal freezer. Saturated salt water freezes at about -21 Celsius, which is a bit beyond the capacity of the average home freezer. If you put less salt in, the freezing point will be higher, but the density will be lower, so it may not sink. Saturated sugar water will still freeze at about -10 Celsius, so you can easily make nice dense sugar-ice cubes in your home freezer.
A neat party trick - make a tray of normal ice cubes and a tray of sugar water ice cubes, and put one of each into the drinks. The plain water cube floats, the sugar water cube sinks, and is perfectly safe to drink as it melts. (Please don't try this with a good single malt scotch though - save it for the soft drinks and cocktails!)
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