Child seat (or rack) at the seat post
The closest thing I have seen is the WeeRide Kangaroo that places the child in front of you.  the support bar attaches to the seatpost and to the head tube, so if you had a second seat post you could leave the bar attached to that end and just connect it at the head tube. 


I don't know of anything that attaches just to the seat post, as the physics involved would cause pretty high torsional force at the point of attachment.

See this related question on toddler seat v. trailer for other child carrying options.