Positron Annihilation Lifetime Spectroscopy (PALS) is a diagnostic method used mostly in material science to investigate solid-state materials' microstructure by measuring the positron lifetime in the material. Typical analog electronics-based PALS experiment is complicated to set up. We report the development of a PALS experimental setup which encompasses organic scintillators and fast digitizers. We interpolated the digital waveform to recover the pulse shape and implemented a constant-fraction discrimination (CFD) timing algorithm to calculate the pulse arrival time. We compared the time resolution performance of three different organic scintillator pairs: BC418, EJ276, and EJ309. We achieved an excellent time resolution of 194.5 1.2 ps using BC418 scintillators, which allows for discrimination ±between different positron lifetime components. We used the optimized experimental setup and used it to determine the lifetimes of positron in two quartz samples. The measured positron lifetimes in quartz are 157 ± 1 ps, 285 ± 1 ps and 1.115± 1 ns, which compares well with the positron annihilation lifetime that characterizes quartz. The system will be used to investigate the nature and density of defects in scintillation crystals.