The effects of vibrational motions on dynamic Stark-induced π-electron rotations in a low-symmetry aromatic ring molecule are theoretically studied in the adiabatic approximation. We adopt a simplified three-electronic state model with a few vibronic states. A pair of the lowest vibronic states in two electronic excited states is set degenerate by irradiation of two linearly polarized UV lasers. The resultant degenerate state is named the dynamic Stark-induced degenerate vibronic state (DSIDVS). The laser parameters (intensities and central frequencies) are determined under the conditions of DSIDVS formation. The aromatic ring molecules of interest are supposed to belong to the weak coupling case. The analytical expressions for the DSIDVS and coherent angular momentum LZ(t) are derived in the displaced harmonic oscillator (DHO) model. Two horizontal potential displacements (δα, δβ) between the two electronic excited states (α and β) and the ground state are the parameters in the DHO model. The LZ(t) calculated with δα = δβ is characterized by a regular sequence of the angular momentum pulses with a positive (or negative) constant. For a more general case with δα ≠ δβ, the regular sequence is broken down because of the contribution of the first excited vibronic state in each electronic state to LZ(t).