Allotropes of carbon conductivity
In charcoal and graphite, conjugated pi systems (the molecule orbital configuration found in carbon-carbon double bonds) act as the conductive band, where electrons can move freely. 

In diamond, all bonds are SP3 hybrid bonds (the molecule orbitals found in single bonds). Therefore, no pi systems and thus no conductive band exists. 

Edit (after  Jon Custer's comment, thanks): Wikipedia says: Except for most natural blue diamonds, which are semiconductors due to substitutional boron impurities replacing carbon atoms, diamond is a good electrical insulator, having a resistivity of 100 GΩ·m to 1 EΩ·m[28] (1011 to 1018 Ω·m). Thus it is possible to dote diamonds with boron to make them more conductive.