The author reports quite accurate calculations on the rotationally elastic, inelastic and summed differential, integral, momentum transfer and energy-loss cross sections for the positron-CO scattering below the positronium formation threshold (7.2 eV). In the body-fixed adiabatic nuclei approximation, a single-centre expansion scheme is used to solve the scattering problem in the close-coupling theory. Fully converged cross sections are obtained via the multipole-extracted adiabatic nuclei (MEAN) method. The polarisation effects are included approximately in a parameter-free way via the positron correlation polarisation (PCOP) potential proposed by the author. The PCOP model is based on the short-range correlation energy, in corr, of one positron in a homogeneous electron gas of the target. In the outside region, the in corr, is joined smoothly with the correct asymptotic form of the polarisation interaction, where they cross each other for the first time. The analytic form of in corr is derived from variational calculations including full positron-electron interactions in the Hamiltonian. The new PCOP results are compared with the author's earlier calculations based on the electron correlation polarisation (ECOP) potential and the R-matrix results of Tennyson and Morgan (1987). The PCOP total cross sections are in very good agreement with the measurements in the whole energy region considered: in particular, at very low energies (below 2 eV), where the ECOP values are in disagreement with experiment. The author's rotationally inelastic cross sections are also in good agreement with the R-matrix calculations.