We report on the design and characterization of a modular γ-ray detector assembly developed for accurate and efficient detection of coincident 511 keV back-to-back γ-rays following electron-positron annihilation. Each modular detector consists of 16 narrow lutetium yttrium oxyorthosilicate scintillators coupled to a multi-anode Hamamatsu H12700B photomultiplier tube. We discuss the operation and optimization of 511 keV γ-ray detection resulting from testing various scintillators and detector arrangements concluding with an estimate of the coincident 511 keV detection efficiency for the intended experiment and a preliminary test representing one-quarter of the completed array.