Is inviting people via Twitter to pray Qiyam al-Layl at a specific time (2:00 AM every night) considered a sound practice, or does it fall under the category of bid‘ah (innovation)?

There is no harm in reminding colleagues and encouraging them to perform Qiyam al-Layl (night prayer), citing the Prophet's action of waking his wives for prayer. Furthermore, setting a specific time for Qiyam is not an innovation (bid'ah), especially if that time is most suitable for the worshipper. Islamic law has also encouraged praying in the early part of the night for those who fear they might not be able to wake up in its latter part.