We analyze a single-level quantum system placed between metallic leads and strongly coupled to a localized vibrational mode, which models a single-molecule junction or an STM setup. We consider a polaron model describing the interaction between electronic and vibronic degrees of freedom and develop and examine different truncation schemes in the equation-of-motion method within the framework of nonequilibrium Green functions. We show that upon applying gate or bias voltage, it is possible to observe charge-bistability and hysteretic behavior which can be the basis of a charge-memory element. We further perform a systematic analysis of the bistability behavior of the system for different internal parameters such as the electron-vibron and the lead-molecule coupling strength.