Yes, but only because you can't sell them!
Just read the absolutely captivating article in The Atlantic Monthly about the value of diamonds as an investment tool. The article http://www.theatlantic.com/doc/print/198202/diamond was written in 1982, but a casual Google search on "historical proces of diamonds" quickly confirms that all the basic numbers are still true, as well as its central premise, which is that diamonds is just about a notch below fertilizer as far as the quality of investment goes.
This is what they say, in short...
First, the diamonds are not actually all that rare. They were, before the beginning of the 20th century. But the since discovered reserves in Africa, Russia, and Australia are pretty big. What's more, the amount of diamonds that is held privately (extracted from these mines over the last 100 years) is astounding.
The diamond market is wholly owned by DeBeers. They fix the price by limiting production, marketing the diamonds as essentially a requirement for marriage in US and Japan (and thus attaching the "sentimental value" to them which is well beyond the real value).
Most importantly, they limit the liquidity of the market, which prevents the influx of second-hand diamonds which would certainly drop the price.
This is where it becomes really fun. How do you prevent the private diamonds from being sold? The scheme is brilliant: if you make a spread between retail and wholesale price huge, people - who paid the retail price when they acquired the stones - would find it very difficult to sell them, because when selling, they would be paying the wholesale price.
And this wholesale price is 2-3 times less than the retail.
In addition, DeBeers makes it hard for dealers to pay even the wholesale price: when dealers get their stones from DeBeers, they get them on consignment: they pay DeBeers when the diamonds are sold. There is no capital on their own involved. But if the dealer is buying the stone from the street, they have to put up their own capital.
The net result? That stone for which you paid $25000 at Costco? If you can get $7000 back for it, consider yourself lucky!
And based on the historical trends (http://minerals.usgs.gov/ds/2005/140/diamondindustrial.pdf), it will not be until the Universe collapses and is reborn in the next Big Bang that the prices will get to the levels where the investment will recoup itself :-).