The star formation histories (SFHs) of galactic stellar haloes offer crucial insights into the merger history of the galaxy and the effects of those mergers on their hosts. Such measurements have revealed that while the Milky Way's most important merger was 8-10 Gyr ago, M31's largest merger was more recent, within the last few Gyr. Unfortunately, the required halo SFH measurements are extremely observationally expensive outside of the Local Group. Here, we use asymptotic giant branch (AGB) stars brighter than the tip of the red giant branch (RGB) to constrain stellar halo SFHs. Both stellar population models and archival data sets show that the AGB/RGB ratio constrains the time before which 90 per cent of the stars formed, t90. We find AGB stars in the haloes of three highly inclined roughly Milky Way-mass galaxies with resolved star measurements from the Hubble Space Telescope; this population is most prominent in the stellar haloes of NGC 253 and NGC 891, suggesting that their stellar haloes contain stars born at relatively late times, with inferred t90 ∼6 ± 1.5 Gyr. This ratio also varies from region to region, tending towards higher values along the major axis and in tidal streams or shells. By combining our measurements with previous constraints, we find a tentative anticorrelation between halo age and stellar halo mass, a trend that exists in models of galaxy formation but has never been elucidated before, i.e.The largest stellar haloes of Milky Way-mass galaxies were assembled more recently.