I use the Contec CMS50E pulse oximeter and put it into record mode and sleep with it on my finger. OK, so how do I not have it fall off at night? I tape it on...
I tear two 0.25" wide strips of medical tape about 4" long. I put on the CMS50E then drape the center of the tape over my finger and
attach the tape ends on the underside of the pulse ox, then repeat such
that the 2nd piece of tape comes up from under wrapping my finger and
the ends are on the top of the pulse ox (or vise-versa, as shown). I can
use the tape tension to control how tight the pulse ox is clamping on
my finger. The two pieces of tape last a couple weeks before needing to
tear off a couple more strips. I have great control over tension of
the clamping-on of the device, from crushing to flippy-floppy and
everywhere between. Try it. It won't come off.