We study optically the coherent evolution of trions and excitons in a δ-doped 3.5-nm-thick ZnO/Zn0.91Mg0.09O multiple quantum well by means of time-resolved four-wave mixing at a temperature of 1.5 K. Employing spectrally narrow picosecond laser pulses in the χ(3) regime allows us to address differently localized trion and exciton states, thereby avoiding many-body interactions and excitation-induced dephasing. The signal in the form of photon echoes from the negatively charged A excitons (TA, trions) decays with coherence times varying from 8 up to 60 ps, depending on the trion energy: more strongly localized trions reveal longer coherence dynamics. The localized neutral excitons decay on the picosecond time scale with coherence times up to T2=4.5 ps. The coherent dynamics of the XB exciton and TB trion are very short (T2<1 ps), which is attributed to the fast energy relaxation from the trion and exciton B states to the respective A states. The trion population dynamics is characterized by the decay time T1, rising from 30 to 100 ps with decreasing trion energy.