Carbon monoxide cation (CO⁺) plays a dominant role in some astrophysical atmosphere environments, and theoretical research on its opacity is crucial for modeling radiative transport. In this work, based on experimentally observed vibrational energy levels of the X²Σ⁺, A²Π, and B²Σ⁺ electronic states of CO⁺, the potential energy curves are improved and constructed using a modified Morse (MMorse) potential function, then the vibrational energy levels and spectroscopic constants are extracted. In the meantime, the internally contracted multireference configuration interaction (MRCI) method with Davison size-extensivity correction (+Q) is used to calculate the potential energy curves and transition dipole moments. The refined MMorse potential shows excellent agreement with the computed potential energy curves, while the spectroscopic constants and vibrational levels indicate strong consistency with existing theoretical and experimental data. The opacities of the CO⁺ molecule is computed at different temperatures under the pressure of 100 atm. The result shows that as temperature rises, the opacities of transitions in the long-wavelength range increases because of the larger population on excited electronic states at higher temperatures. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00136.