Data are now available on the Sun-like, p-mode oscillations of a growing number of late-type stars. With extension of these observations to dedicated, long-term campaigns, it will soon become possible to probe acoustically magnetic activity, and stellar cycles, by observation of systematic shifts in the mode frequencies giving additional information to the stellar dynamo theorists. Here, we use model computations of the damping rates of stochastically excited radial p modes to make predictions of the precision with which it will be possible to measure stellar-cycle frequency shifts of Sun-like stars along the lower main sequence. We assume the first analyses will average shifts across the most prominent modes to reduce uncertainties. We also make some predictions of the expected frequency shifts, based on existing stellar Ca ii H& K data. Our main conclusion is that the basic properties of the acoustic signatures of the cycles should be measurable to reasonably high precision given only a few multimonth segments of data. It should also be possible to make inference on the surface distribution of the activity, through measurement of shifts of modes of different degree. Our computations also reveal an interesting feature in the predicted appearance of the acoustic mode spectra of stars cooler than about 5400 K: the modelled power spectral density of the modes shows two maxima, at different frequencies. By computing average shifts of modes across the two maxima, where the signal-to-noise ratio is highest, it should be possible to get the first measures of the frequency dependence of the p-mode shifts. This dependence provides information on the mechanism responsible for driving these shifts.