R-matrix calculations combined with the adiabatic nuclei approximation are used to compute electron-impact rotational excitation rates for three closed-shell diatomic cations, HeH⁺, CH⁺, ArH⁺. Comparisons with previous studies show that an improved treatment of threshold effects leads to significant changes in the low temperature rates; furthermore the new calculations suggest that excitation of CH⁺ is dominated by ΔJ = 1 transitions as is expected for cations with a large dipole moment. A model for ArH⁺ excitation in the Crab nebula is presented which gives results consistent with the observations for electron densities in the range 2-3 × 10³ cm^-3.