Pretty diamonds usually form in Earth's mantle and are brought up to the surface in volcanic eruptions. They are mined from volcanic pipes such as kimberlites, and even though some of them are named like they're impact craters (like the Crater of Diamonds State Park) they are not actually impact craters.
Other stuff
There is one notable occurrence of an impact crater that did cause economic mineralisation of something: the Sudbury Igneous Complex, or the Sudbury Basic, in Canada. In here, a meteorite impact caused melting of the crust and the formation of a nickel deposit. Currently, nickel, copper and some noble metals are mined from there. Even though it has been known for more than 100 years, only in the past 30 years or so the impact origin of it has been fully accepted.
As for economically important placer occurrences of industrial-grade diamonds, their source is still controversial. Geochemistry may prove a kimberlite source for these diamonds....just like those in South Africa.
A little bit of lunar scenery, here on earth.