An irreverant/fantasy show with sypathetic well-intentioned protagonists, at minimum understandable volume, with characters and plotlines that invite analysis. Something about the pointlessness of studying a fantasy universe is a quite effective sleep aid. Various Star Trek series, Futurama, X-Files, Grimm, Family Guy...
For shows that are a great fit except for a few segments (boisterous theme songs, jarring fight scenes, etc) the PotPlayer Skip Playback function (hotkey ') is super useful. Also I have a basic script that gradually mutes the volume after 40 minutes.
From Wordnik.com: ennui (on WEE) - noun - A painful or wearisome state of mind due to the want of any object of interest, or to enforced attention to something destitute of interest; the condition of being bored; tedium. ... A gripping listlessness or melancholia caused by boredom. ... from Old French enui, from ennuyer, to annoy, bore; see annoy.