Many sensory neurons encode temporal information by detecting coincident arrivals of synaptic inputs. In the mammalian auditory brainstem, binaural neurons of the medial superior olive (MSO) are known to act as coincidence detectors, whereas in the lateral superior olive (LSO) roles of coincidence detection have remained unclear. LSO neurons receive excitatory and inhibitory inputs driven by ipsilateral and contralateral acoustic stimuli, respectively, and vary their output spike rates according to interaural level differences. In addition, LSO neurons are also sensitive to binaural phase differences of low-frequency tones and envelopes of amplitude-modulated (AM) sounds. Previous physiological recordings in vivo found considerable variations in monaural AM-tuning across neurons. To investigate the underlying mechanisms of the observed temporal tuning properties of LSO and their sources of variability, we used a simple coincidence counting model and examined how specific parameters of coincidence detection affect monaural and binaural AM coding. Spike rates and phase-locking of evoked excitatory and spontaneous inhibitory inputs had only minor effects on LSO output to monaural AM inputs. In contrast, the coincidence threshold of the model neuron affected both the overall spike rates and the half-peak positions of the AM-tuning curve, whereas the width of the coincidence window merely influenced the output spike rates. The duration of the refractory period affected only the low-frequency portion of the monaural AM-tuning curve. Unlike monaural AM coding, temporal factors, such as the coincidence window and the effective duration of inhibition, played a major role in determining the trough positions of simulated binaural phase-response curves. In addition, empirically-observed level-dependence of binaural phase-coding was reproduced in the framework of our minimalistic coincidence counting model. These modeling results suggest that coincidence detection of excitatory and inhibitory synaptic inputs is essential for LSO neurons to encode both monaural and binaural AM sounds.