Diamonds do not come from coal, and the diamond forming process generally does not even involve a form of coal. Coal is a rock that is formed by sediment, and diamonds are formed through igneous sources.
Diamonds are generally formed in one of four ways, but the most common way is the formation of diamonds in the mantle of the earth. In order for diamonds to form, extreme temperature conditions must be present. These conditions are only found in the mantle of the earth around 90 miles below the surface. There are only specific spots in the mantle where the diamond-forming process is possible due to conditions that involve atmospheric pressure and an exact temperature.
It is important to note that while diamonds do not need coal to form, there is a small possibility that coal could play a role in the way that diamonds are brought to the Earth's surface and, subsequently, into the commercial market they play a role in today. For diamonds to come to the surface, there needs to be some sort of carbon reaction. There is a possibility that coal is the carbon that is needed for diamonds, but the more likely source of carbon for diamonds is the tectonic shifting of plates in the underground area where they are located.