We report an updated measurement of the νμ-induced, and the first measurement of the νˉμ-induced coherent charged pion production cross section on 12C nuclei in the T2K experiment. This is measured in a restricted region of the final-state phase space for which pμ,π>0.2 GeV, cos(θμ)>0.8 and cos(θπ)>0.6, and at a mean (anti)neutrino energy of 0.85 GeV using the T2K near detector. The measured νμ CC coherent pion production flux-averaged cross section on 12C is (2.98±0.37(stat.)±0.31(syst.)+0.49−0.00(Q2model))×10−40cm2. The new measurement of the νˉμ-induced cross section on 12C is (3.05±0.71(stat.)±0.39(syst.)+0.74−0.00(Q2model))×10−40cm2. The results are compatible with both the NEUT 5.4.0 Berger-Sehgal (2009) and GENIE 2.8.0 Rein-Sehgal (2007) model predictions