If dark matter self-annihilates into neutrinos or a second component of ("boosted") dark matter that is nucleophilic, the annihilation products may be detected with high rates via coherent nuclear scattering. A future multi-ten-tonne liquid xenon detector such as darwin, and a multi-hundredtonne liquid argon detector, argo, would be sensitive to the flux of these particles in complementary ranges of 10-1000 MeV dark matter masses. We derive these sensitivities after accounting for atmospheric and diffuse supernova neutrino backgrounds, and realistic nuclear recoil acceptances. We find that their constraints on the dark neutrino flux may surpass neutrino detectors such as Super-Kamiokande, and that they would extensively probe parametric regions that explain the missing satellites problem in neutrino portal models. The xenont and borexino experiments currently restrict the effective baryonic coupling of thermal boosted dark matter to 10 − 100 × the weak interaction, but darwin and argo would probe down to couplings 10 times smaller. Detection of boosted dark matter with baryonic couplings ∼ 10 −3 − 10 −2 × the weak coupling could indicate that the dark matter density profile in the centers of galactic halos become cored, rather than cuspy, through annihilations. This work demonstrates that, alongside liquid xenon, liquid argon direct detection technology would emerge a major player in dark matter searches within and beyond the wimp paradigm.