Rast & Toomre (1993, Paper I) examined the effects of ionization-state changes on the stability, flow asymmetry, and flux transport properties of two-dimensional compressible convection. Here we employ the same single-atomic-level hydrogen model and analyze vigorously time-dependent nonlinear solutions. Ionization- state-dependent variations in thermal diffusivity of the fluid can result in thermal boundary-layer instability and plume formation. The interval between pluming events depends on the growth rate of the instability and both the scale and the velocity of the underlying convective motions. Such instabilities can occur at either boundary, depending on the positioning of the partially ionized region within the domain. Here we concentrate on simulations in which the instability is manifest in the upper thermal boundary layer, and results in cool plume formation. Temperature fluctuations and associated buoyancy forces in the plumes are maintained as long as heat exchange and compressional heating result primarily in ionization of the fluid rather than in temperature equilibration, and this can lead to supersonic vertical flows in an otherwise subsonic flow field. These flows serve to excite acoustic oscillations, the phase of which can be abruptly altered by subsequent plume events. For high rates of plume initiation, the fundamental acoustic period of the domain is greater than the time span between two descents. Such ionization effects are expected to influence the dynamics of granulation and acoustic mode excitation in the Sun and other stars, and likewise the coupling of convection with pulsations that occurs in stars such as white dwarfs and Cepheid variables. Additionally, it is possible that thermal instabilities analogous to those seen in these simulations occur not only in the photosphere but also at the base of stellar convective envelopes owing to temperature-sensitive variations in the radiative conductivity of fluid there.