In photoluminescence experiments the D-II center shows phonon replica with carbon-like vibrational modes above the highest bulk phonon mode. We have performed ab initio calculations of the localised vibrational modes (LVM) of defects in SiC possessing carbon bonds. We find that the di-carbon antisite C-sp, (Csi(100)) (two carbon atoms at a silicon site) exhibits a LVM spectrum compatible with that of the D-II center in all available charge states. Its formation energy compares to that of the most abundant carbon interstitials, namely the carbon split-interstitial and the carbon-silicon split-interstitial. We discuss the structural, electronic and vibrational properties of this defect in 3C-SiC and also present the first results for 4H-SiC.