In trying to solve this same problem, I purchased a small coleman ice chest. It measures approximately 18" long by 10.5" wide by 13" tall and fits very snugly between the middle row seats. I purchased it at the local Walmart for about $10 six months ago or so.
It has turned out to be a much better solution than I had hoped:
1) it is a good sized cooler for long family trips;
2) with the cooler closed it provides a nice flat surface just above the seat level (perfect when they are sittinging in their car seats) for my two boys to place their toys. It also creates an area between the car seat and the cooler to put drinks (little guy cannot reach the cup holder on the side edge of his seat) and other stuff.
3) the top can be turned over to reveal 4 cup holders and a recessed area to put food, etc. (works great for holding hamburgers, french fries and ketchup and allows dad to keep on driving). The top is attached to the side by two plastic hinges that let the lid flip up like most coolers. I just pulled the screws out and removed the hinges.
4) When not used as a cooler, the ice chest can be used to store toys, etc.
5) And last, but not least...It is a good sized cooler for every day use. It is easy to put in and take out.
Hope this helps.