Neutrino-induced coherent charged pion production on nuclei ν(-)μA→μ±π A is a rare, inelastic interaction in which a small squared four-momentum |t| is transferred to the recoil nucleus, leaving it intact in the reaction. In the scintillator tracker of MINERvA, we remove events with evidence of particles from nuclear breakup and reconstruct |t| from the final-state pion and muon. We select low |t| events to isolate a sample rich in coherent candidates. By selecting low |t| events, we produce a model-independent measurement of the differential cross section for coherent scattering of neutrinos and antineutrinos on carbon. We find poor agreement with the predicted kinematics in neutrino generators used by current oscillation experiments.