The detection of Lyα emitting galaxies (LAEs) puts severe constraints on the reionization history. In this paper, we derive the properties of very high-z LAEs predicted in the only two reionization scenarios shown in a previous paper to be consistent with the current data on 15 independent evolving global (or averaged) cosmic properties regarding luminous objects and the intergalactic medium and the optical depth to electron scattering of ionized hydrogen to cosmic microwave background photons: one with a monotonic behavior, which is completed by z = 6, as commonly considered, and another one with a nonmonotonic behavior with two full ionization events at z = 6 and z = 10. We find that the Lyα luminosity functions of very high-z LAEs are very distinct in those two scenarios. Thus, comparing these predictions to the observations that will soon be available thanks to new instruments such as the James Webb Space Telescope, it should be possible to unveil the right reionization scenario. In the meantime, we can compare the predicted redshift distribution and UV (or Lyα) luminosities of very high-z LAEs to those of the few objects already observed at z > 7.5. By doing that, we find that such data are in tension with the single reionization scenario, while they are fully compatible with the double reionization scenario.