I had perhaps the most inelegant solution ever when taking my niece across the country. I used a portable DVD player and just put it on the counter next to the sink so she could see it from the 50 couch. Just from the rubber feet it seemed like it would stay, so I added an elastic loop string from the faucet to the fridge hinge- loose so there wasn't any pressure. I dropped one of the elastic loop halves on each side of the screen (one in back and one across the base) just to keep it from flying off the counter on a bump or turn.
So on to useful information... RAM makes great solid mounts. I use one for my GPS but it would be a good place to look for something for a DVD player off the wall or from a ceiling cross piece. You could even suction cup to the counter if you don't want to go the hillbilly bungie route.