Coincidence Doppler-broadening spectroscopy was applied to C60 and C70 fullerenes and other carbon phases, such as nanotubes and graphites. Remarkable differences were observed in the Doppler-broadening of the positron annihilation gamma-rays in these materials, which reflect the different densities distribution of the momentum for electrons annihilated with positrons. This would be caused by the different composition of the pi and sigma electrons in annihilation with positrons. This result shows the sensitivity of the coincidence Doppler-broadening method to determine the density distribution of electrons sampled by positrons.