  The carbon monoxide rovibrational emission from discs around Herbig Ae stars
and T Tauri stars with strong ultraviolet emissions suggests that fluorescence
pumping from the ground X1 Sigma+ to the electronic A1 Pi state of CO should be
taken into account in disc models. We implemented a CO model molecule that
includes up to 50 rotational levels within nine vibrational levels for the
ground and A excited states in the radiative photochemical code ProDiMo. We
took CO collisions with hydrogen molecules, hydrogen atoms, helium, and
electrons into account. We estimated the missing collision rates using standard
scaling laws and discussed their limitations. UV fluorescence and IR pumping
impact on the population of ro-vibrational v > 1 levels. The v = 1 rotational
levels are populated at rotational temperatures between the radiation
temperature around 4.6 micron and the gas kinetic temperature. The UV pumping
efficiency increases with decreasing disc mass. The consequence is that the
vibrational temperatures, which measure the relative populations between the
vibrational levels, are higher than the disc gas kinetic temperatures
(suprathermal population). Rotational temperatures from fundamental transitions
derived using optically thick 12CO lines do not reflect the gas kinetic
temperature. CO pure rotational levels with energies lower than 1000 K are
populated in LTE but are sensitive to a number of vibrational levels included
in the model. The 12CO pure rotational lines are highly optically thick for
transition from levels up to Eupper=2000 K. (abridged)
