Lay on your back and you can use any headphone.
There are speakers that fit under the pillow. They provide poor mono.
Why not a bedside audio player?
Erik - See link above to HeadFi.org and info on the Yuin PK earbuds. They are not IEMs nor ar they conventional headphones. The Yuins have very good sound and reasonable bass for their size. They do require lengthy break in for what bass they produce to be realized. I own the PK2s and listen to Pandora while falling asleep. They are extremely comfortable. I have woken up, forgotten I had them on and was startled to hear music playing in the room. They "do" a big soundstage. Worth consideration, I think. Good luck with what sounds like a procedure you'd probably rather avoid.