In the present paper we describe in detail results of numerical calculations for eigen oscillations of the shear Alfv¿n wave coupled with the ionospheric ion dirft in the presence of the steady electric field. The instability mechanism has been discussed in a companion paper (Tamao and Miura, this issue). For a model magnetosphere with a nonuniform density distribution along dipole magnetic field lines, together with ionospheric boundary conditions through which the coupling with the ion drift wave is taking place, we have solved numerically a system of differential equations describing the localized torsional oscillations of field lines. Dependences of the eigenfrequency and the growth (or damping) rate of oscillations on the height-integrated ionospheric conductivity are examined, and it is shown that the nighttime oscillations exhibit a stronger instability than those for daytime. There is a minimum threshold intensity of the steady electric field and a maximum scale length in the north-south direction of the localized oscillation in the ionosphere for occurrence of the instability. These are ten to a few tens of mV/m and a few tens of kilometers, respectively. The maximum scale length decreases with decreasing invariant latiutde of the field line, while the peak value of the growth rate increases. Eigen function distributions along the field line are also determined, which makes it possible to infer dependences of perturbations at the level just above the ionosphere on the Pedersen conductivity in the ionosphere.