Lists of who you might be looking for may be helpful. I presume you're not straying into fairy-tale characters (Little Red Riding Hood, the Seven Dwarves, Aladdin, Three Bears etc) - because some of those guys should be easy - but I guess you might be looking for:
Little Boy Blue;
Little Jack Horner;
Little Miss Muffit;
Georgie Porgie;
Jack and Jill;
Jack B. Nimble;
Aiken Drum;
Peter Piper (not exactly a nursery rhyme I know);
Polly and Suky;
Mary, quite contrary;
Mary, with her little lamb;
Dr Foster.
I'm sure there's dozens I haven't thought of.
Some of those you would have to greenstuff I would think - Aiken Drum springs to mind, can't recall any figures with a cheese hat, meat waistcoat and ladle guitar, but others might be failry easy to get, like Dr Foster - a fat man with a bag, I'd have thought there would be Dr Watson figures out there you could use - or Polly and Suky maybe, possibly with a kettle? I'm sure Foundry do a couple of packs of Victorian servants, some of them might be suitable (obviously we don't tell the children that Dr Foster has caught syphilys, and Polly and Suky are prostitutes, that would never do).