Diamonds are a rare and valuable resource that you can get from Stone Tali and Ore Deposits.
Sources of Diamonds
Diamonds have a rare chance of coming from Rare Ore Deposits, and an extrememly rare chance of coming from normal Ore Deposits.
You also have a chance of getting diamonds when you defeat Stone Tali. They are most common from Rare Stone Tali, which have a 50% chance of dropping a diamond, and a very low chance of dropping two diamonds.
You can also purchase diamonds from Gonguron's diamond shop in Goron City after you complete the Fire Temple.
Recommended Method for Farming Diamonds
There are only 14 Rare Stone Tali, but with a 50% chance of getting a diamond, they are the best source for farming diamonds. See the List of Stone Talus (Rare) for the locations of all 14 Rare Stone Tali.