Single-crystalline, homoepitaxial ZnO films doped with tri- and tetravalent cations were fabricated by liquid phase epitaxy (LPE) from low-temperature lithium chloride solution. The LPE is applied as a fast-screening tool to obtain mechanically undisturbed (0001) surfaces of the undoped and In3+ and Ge4+-doped ZnO films. Time-resolved photoluminescence characteristics upon the excitation by a femtosecond laser pulses are studied. Characteristics of the films are discussed and particularly the effect of In3+ and Ge4+ on the luminescence decay kinetics is examined. We find the double-exponential decay at room temperature consisting of an ultra fast and a slower component with decay times τ around 30-60 and 250-800 ps, respectively. High-intensity emission due to donor-acceptor pair recombination peaking around 420 nm at room temperature is obtained from the Li+, In3+ co-doped ZnO film, which shows the inverse power law decay at longer times.