The frequency analysis of a bistable binary oscillator triggered by a stationary random signal is performed by analyzing the expression for the power spectrum of its output. The oscillator state changes when the input noise exceeds a fixed threshold ΞΈ, which occurs in correspondence of the events produced by an ordinary renewal process. After each state change a fixed refractory time T is to be passed before the output performs a new transition. A theoretical study shows that a coherence resonance (CR) effect appears in the output square wave if the threshold ΞΈ is lower than a positive real value ΞΈ. When the overcoming of the input threshold occurs according to a Poisson process with exponential parameter Ξ±, the regularity is present at the output only if the product Ξ±T exceeds β 2 -1. The value of the characteristic frequency increases rapidly with Ξ±T towards its asymptotic value 1/(2T). The same probabilistic approach is then adopted to perform the spectral analysis of a set of uncoupled binary oscillators, sharing the same refractory time T and the same input random signal. Under mild assumptions the whole system behaves as a single oscillator, whose output is amplified proportionally to the number of elements involved.