Understanding the nature of the photoexcitation and ultrafast charge dynamics pathways in organic halide perovskite superlattices is key for their potential applications as tunable light emitters, photon harvesting materials and light-amplification systems. In this work we apply two-dimensional coherent electronic spectroscopy (2DES) to track in real time the formation of near-infrared optical excitons and their ultrafast decay into bi-excitons in CH(NH2)2PbI3 nanocube superlattices. On the picosecond timescale, the strong coupling between localized charges and specific lattice distortions leads to the progressive formation of long-lived localized trap states. The analysis of the temperature dependence of the excitonic intrinsic linewidth, as extracted by the anti-diagonal components of the 2D spectra, unveils a dramatic change of the excitonic coherence time across the cubic to tetragonal structural transition. Our results offer a new way to control and enhance the ultrafast coherent dynamics of photocarrier generation in hybrid halide perovskite synthetic solids.