Motivated by the recent experimental observation of exclusive c events at the Tevatron, we revisit earlier studies of central exclusive scalar c0 meson production, before generalising the existing formalism to include c1 and c2 mesons. Although c0 production was previously assumed to be dominant, we find that the c1 and c2 rates for the experimentally considered c ! J/ ! μ+μ− decay process are in fact comparable to the c0 rate. We have developed a new Monte Carlo event generator, SuperCHIC, which models the central exclusive production of the three c states via this decay chain, and have explored possible ways of distinguishing them, given that their mass differences are not resolvable within the current experimental set-up. Although we find that the severity of current experimental cuts appears to preclude this, the acceptance does not change crucially between the three states and so our conclusions regarding the overall rates remain unchanged. This therefore raises the interesting possibility that exclusive c1 and c2 production has already been observed at the Tevatron.