I amuse myself when singing nursery rhymes to DD by making one nursery rhyme segue to the next by some sort of theme. So for instance, I might start with London Bridge is Falling Down, then go:
London's Burning (London connection)
Jack and Jill (water)
Miss Polly had a Dolly (medical treatment)
Polly put the kettle on (Polly)
I'm a little tea pot (tea)
And on the basis that I find 'I'm a little tea pot' to be a tough one to follow on from, who wants to play? Just add the song that you would go to from the previous poster's suggestion.