The Haier 7" LCD TV is a good fit. It accepts AV input (in addition to coax, but we don't care about that). This is a discontinued model, but is available at Amazon.com for $50 including shipping. It is about 1" thick and weighs 1.3 lbs. It includes a rechargeable battery and a charger. (To me the battery side is very important.)
Caveats: Some people have reported white(ish) screen and a few dead pixels. Overall, based on the reviews, my sense is that you will have a close to 3:1 chance you will get a piece that works. Make sure you buy it from Amazon so you can easily return a bad piece.
This item is available from other vendors for up to $100. Over at Amazon, you will also find other brands that can work: Axion, Viore, Vizio, and Coby; all priced higher. Axion appears closest to Haier; Coby is the thickest and heaviesst. Vizio appears to be the best (thinner, lighter, all around better), but is also expensive at ~$93.
Here is a direct link to the Vizion model: http://amzn.to/pPn5Gr