My cousin had one similar to what ncjay posted, though the seat was wide enough for my cousin who was a little chunk at the time, and a skinny kid to both ride, however it may not have officially been a "2 seater," but we made it one.
We too had no safety gear, grandma bought us all bike helmets for Christmas one year, but short of trying them on when we opened them, they were rarely on our heads for any of our antics.
A note on the "1 wheel drive karts," if your kids are anything like we were, they'll find a way to do something fun and stupid with even the safest kart.
A friend from school's little brother had a similar 1 seater, 1 wheel drive, kart to the one ncjay posted, but with the added "safety" of a roll bar. Just a single hoop behind the seat, no cage, and no triangulation to speak of, it may have had some additional bracing, but all I remember for sure is it had a roll bar. While that roll bar's design intent was obviously for safety, we found it also served as an excellent hand hold for some one to ride standing up on the back. Additionally with someone standing on the back it was real easy for the "rear passenger" to shift their weight around and make the thing pop a wheelie, whether the pilot of the kart wanted to or not. Being 1 wheel drive, once the front end was off the ground, it instantly became a spinning, donut, machine, spinning more or less in place until the pilot let off the throttle, or one or both occupants were flung from the kart.
Once this trick was discovered, the challenge then became to jump on the kart as it passed by and cause it to "spin out," especially when my friend's little brother was piloting the thing.
We all eventually got into ATVs, my friends all had 3 wheelers or quads of some sort, and I had a slow as molasses Kawasaki Mule, though I still managed to go over some sweet jumps even in the Mule.