This probably isn't quite a true *kids'* ditty -- it was a novelty song about kids' ditties that got some radio play circa 1963. Sort of a laundry list of couplets -- the only ones I still remember were chanted, rapidly:
"Ladies and gentlemen, take my advice!
Pull down your pants and slide on the ice!"
"Oh what a face! Oh what a figure!
Two more legs and you'll look like Trigger!" -- with a bar of clippety-clop sound after that one.
There would be a few couplets and then a chorus. The final chorus ended with
"...when youuuuu were a kid!"