CERN-LHC. Measurement of J/PSI and PSI(2S) production cross sections in proton-proton collisions at a centre-of-mass energy of 7 TeV. The data sample used, collected in 2010, has a total integrated luminosity of 37 pb-1. This extends the previously published CMS analysis (EPJ C71(2011)1575) with a larger amount of statistically independent data. Cross sections are extracted for both prompt and non-prompt (via b-hadron decay) production with both acceptance corrected and uncorrected data given. Cross section ratios are presented as well as estimates of the effects of four different poarization scenarios for b-hadron decay (fully longitudinal and transvere in both the Collins-Soper and Helicity frames). ; Other ; The (unpolarised) acceptance corrected J/PSI cross section times branching ratio to MU+ MU- for (PROMPT) and NON-PROMPT) production in the |rapidity| bin 1.6-2.1.