We present a study of J/psi and psi(2S) production in ppbar
collisions, at sqrt s = 1.8 TeV with the CDF detector at Fermilab.  The J/psi
and psi(2S) mesons are reconstructed using their mu^+mu^- decay modes.  We
have measured the inclusive production cross section for both mesons as a
function of their transverse momentum in the central region, |eta| < 0.6.  We
also measure the fraction of these events originating from b hadrons.  We thus
extract individual cross sections for J/psi and psi(2S) mesons from b-quark
decays and prompt production.  We find a large excess (approximately a factor
of 50) of direct psi(2S) production compared with predictions from the color
singlet model.