Eero Aarnio is credited with many shagpad-worthy designs from the 70's, including the abstracted pony-shaped seating unit (it's too unusual to be called a chair) that retails for around $2,100.
If you want a bid or swingin' style for your kid, but you prefer to blow your wad on luxuries like, say, gasoline, you're in luck. The Italian plastic furniture manufacturer Magis introduced two new Eero Aarnio designs as part of the company's Me Too collection of children's furniture. [I posted about the Me Too drawing table by Marcel Wanders last year.] There's an abstracted puppy in molded polyethylene that's available in three kid-friendly sizes in lime green [and sometimes off-white] that runs under $100.
And Aarnio's Trioli chair is an updated barrel chair, with two seating heights, that can rock when you turn it on its side. It comes in red, blue, yellow, or white for around $200.