In the answer to question no. 34325 it says that it is not permissible to sell gold or silver on the Internet. That is because this transaction delays taking possession of the price for the product, which is not permissible when selling gold and silver. 

As for selling diamonds, it is permissible to pay the price in advance or to delay it. 

Based on that, there is nothing wrong with buying or selling them on the Internet. 

But there is another problem, which is that it is difficult to grade diamonds precisely, so they should not be bought except after seeing them, because the grades vary a great deal and the price and the purchaser’s interest in buying may vary accordingly. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

With regard to things of which the quality cannot be known through (general) description only, such as gemstones and pearls and the like, it is not permissible to sell them on the basis of (general) description, because they may vary greatly. One pearl may be worth, for example, a thousand riyals and another may be worth ten riyals, so it is difficult to know the exact quality. So it is essential to grade them precisely so that there will be a clear understanding of the item and there will be no dispute when it is delivered. 

End quote from ash-Sharh al-Mumti‘, 8/150 

Based on that, if it is possible to convey a precise idea of the quality of an item through a description in terms known to people of expertise or if a photograph can be taken and presented in such a way as to convey this precise idea, then there is nothing wrong with selling it on the internet. But if the description is not sufficient and the picture is not sufficient either, then it is not permissible to sell it (on the Internet), because that will lead to disputes between the seller and purchaser in most cases. 

And Allah knows best.