Contrary to popular belief, diamonds do not actually from coal, at least not usually. Coal is a relatively recent phenomenon in geological terms, as it required land plants to live, die, and then be compressed over millions of years. Diamonds are much, much older.
The most common way for diamonds to form is in the Earth's mantle, in particular regions with just the right level of temperature and pressure and sufficient carbon in the surrounding rocks. These regions are most commonly found under the middles of continental plates. We of course could never dig that far down into the mantle; fortunately, volcanic eruptions occasionally bring up parts of the mantle containing these diamonds close to the surface, where we can extract them.
Diamonds can also be formed by the collision of tectonic plates, particularly in subduction zones where an oceanic plate is pushed under a continental plate.
Diamonds can come from meteorites, in one of two ways: Either they can be formed in space by collisions between asteroids, or they can be formed at the moment the meteorite hits the ground and releases all its kinetic energy.
Finally, we can now synthesize diamonds by subjecting graphite or coal to extremely high temperature and pressure. These diamonds are usually small and not very pretty---but they are just as hard as any other diamond. (Large, attractive synthetic gemstones can be produced, they just aren't nearly as common.) In fact, most of the world's diamond consumption is in the form of synthetic diamonds, though not as gemstones but for industrial equipment.