The kinetics of spontaneous composition pattern formation in a quenched alloys under irradiation is numerically studied by means of phenomenological Enrique-Bellon equation for the local concentration field. In the present model the irradiation effect is modeled as a ballistic mixing with an average distance of atomic relocation R and its frequency Γ. Several two-dimensional computer simulations show that the competitive mechanism between phase separation and irradiation-induced mixing might provide a novel way to stabilize and tune the steady-state nanostructures of phase separating materials in some region on (R, Γ) space.