Lithium spin-alignment spectroscopy is presented as an NMR technique for studying slow translational motions in solid and solid-like ionic conductors. We employ phase cycling that allows to measure two-time translational correlation functions via the generation of a pure quadrupolar ordered state. Correlation functions of the crystalline electrolyte Li3Sc2(PO4)(3) were recorded for times ranging from about 0.1 ms to more than 10 s, implying that translational diffusion coefficients smaller than 10(-20) m(2)/s become accessible.