We investigate whether cyclic variations in stellar activity can account for the observed spread in fractional X-ray luminosity, LX/Lbol, for cool stars in the unsaturated range of Rossby number, Ro ≳ 0.1. To address this question, we employ an empirical flux transport model of the stellar surface, incorporating modulations of magnetic flux strength consistent with observed stellar activity cycles. We find that for stellar flux models corresponding to a range ~0.1 ≲ Ro ≲ 2, the LX/Lbol vs. Ro relation matches well the power-law behavior observed in the “unsaturated” regime of cool stars. Additionally, the magnetic activity cycles incorporated into the stellar simulations produce a spread about the power-law relation consistent with the observed spread in unsaturated cool star populations. We find, therefore, that the solar-based flux transport approach employed in this work can reproduce the X-ray luminosity-magnetic activity relation observed across the range of unsaturated late-F, G, K, and M stars, providing support for the hypothesis of a universal dynamo mechanism operating in all unsaturated cool stars. We further conclude that the spread in fractional X-ray luminosity, LX/Lbol, across the unsaturated range of stellar activity corresponding to ~0.1 ≲ Ro ≲ 2 can be explained by the intrinsic variation due to stellar activity cycles.