Kasumi the Invisible Girl is about a school girl who can turn invisible if she holds her breath. As you can imagine, a good scenario for sleepy scenes.
There's a few pages where she's shown unconscious. In on particular scene in volume 1, Kasumi is grabbed by a boy who then hugs her really tightly. This causes her to *nearly* pass out, but not completely. I like the dialogue here.

I found this scene completely at random, by flipping through random manga at a Barnes & Noble.

Source: http://mangafox.me/manga/kasumi/