You hit the nail on the head with the rock 'n play, but you cannot record on it. There are several units on the market that are like you say, a one man band. Boss (Roland) has one called the Jam Station,
Here and they have a couple other that are integrated into their drum machines as well, see the whole Roland lineup
Here. If you're looking for an all in one that you can record on as well as back yourself up, I don't know of any off the top of my head, but I'm sure with a little research to the other brands' websites, you can find something from Yamaha, Korg, or whomever.
Good luck,
Bamm