In this paper, we simulate intermittent turbulence (also known as bursting events) in stably stratified open-channel flows using direct numerical simulation. Clear signatures of this intriguing phenomenon are observed for a range of stabilities. However, the spatiotemporal characteristics of intermittency are found to be strongly stability dependent. In general, the bursting events are much more frequent near the bottom wall than in the upper-channel region. A steady coexistence of laminar and turbulent flows is detected at various horizontal planes in very stable cases. This spatially intermittent pattern is found to propagate downstream and strongly correlate with the temporal evolution of intermittency. Lastly, a long standing hypothesis by Blackadar (1979), i.e., the strong connection between local stability and intermittent turbulence, is corroborated by this modeling study.