Lie on your side and use the hand on the arm that's under your pillow to hold the iPad vertically on the bed. When you doze off, your grip will fail, but then the iPad just falls over on its face, which shouldn't be close enough to hit you in yours unless you're a lot more nearsighted than I am. (It might fall off the bed, though. Not a problem I have because I sleep alone on a queen-size, but I can see how other configurations might cause that issue.)

If you prefer to lie on your back, an articulated arm mounted to the headboard might work; I have one of those, but ended up not actually using it - by the time I'm actually dropping off, I don't want a screen glowing in my face.