I had one on my Europa - 80's roadie. It was similar to the orange one above - clamp on seat tube, seat had two arms that plugged into the clamp providing both location and springing. Worked well. I don't remember the name and that was over 20 years ago so recommendations would be pointless. The concept works though.

My daughter had a different one that I can't recall now. She loved it too though had a tendency to fall asleep and lean over the edge. She graduated to a tag-along bike which suited her and used to drive her brother mad because rather than pedaling and helping, she'd sit there and backpedal

Although I never used it for a child, until he died last year, I used to pull my dog in a kiddie trailer. This clamped onto the chain stay with a rubberised clamp so you didn't need any special fitting on the bike - rock solid, I even hit a post one day and it didn't move. I used to tow that with my Europa (mentioned above). I actually rebuilt the wheels with alloy rims and Swalbe tyres which gave it a much better ride than the cheap wheels it came with.