We derived astroparticle constraints in different dark matter scenarios that are alternatives to cold dark matter (CDM): thermal relic warm dark matter, WDM; fuzzy dark matter, ψDM; self-interacting dark matter, SIDM; sterile neutrino dark matter, νDM. Our framework is based on updated determinations of the high-redshift UV luminosity functions for primordial galaxies to redshift z∼10, on redshift-dependent halo mass functions in the above DM scenarios from numerical simulations, and on robust constraints on the reionization history of the Universe from recent astrophysical and cosmological datasets. First, we built an empirical model of cosmic reionization characterized by two parameters, namely the escape fraction fesc of ionizing photons from primordial galaxies, and the limiting UV magnitude MUVlim down to which the extrapolated UV luminosity functions steeply increased. Second, we performed standard abundance matching of the UV luminosity function and the halo mass function, obtaining a relationship between UV luminosity and the halo mass, whose shape depends on an astroparticle quantity X specific to each DM scenario (e.g., WDM particle mass); we exploited such a relationship to introduce (in the analysis) a constraint from primordial galaxy formation, in terms of the threshold halo mass above which primordial galaxies can efficiently form stars. Third, we performed Bayesian inference on the three parameters fesc, MUVlim, and X via a standard MCMC technique, and compared the outcomes of different DM scenarios on the reionization history. We also investigated the robustness of our findings against educated variations of still uncertain astrophysical quantities. Finally, we highlight the relevance of our astroparticle estimates in predicting the behavior of the high-redshift UV luminosity function at faint, yet unexplored magnitudes, which may be tested with the advent of the James Webb Space Telescope.