Instead of "a song that makes you fall asleep" here are two songs that I can chill out to, or relax, or whatsoever. As this state of mind is normally thought of to be characterised by a low level of activity, no further comments will be added.
BUSH: Letting the cables sleep (from: "The Science of Things")
MOBY: Why does my heart feel so bad?
Disclaimer: this is featured 4 the music only; as the original video is not available on utube, this is just randomly selected (other choices no better)