The Wheels of the Bus Go Round & Round was one we used to sing when I was a toddler. In the next verse the horn on the bus goes honk-honk-honk (or hoot-hoot-hoot, depending on which side of the Atlantic said bus is on), the-doors-on-the-bus-go-in-&-out, the-driver-on-the-bus-says-10-cents/pence-please, the-people-on-the-bus-say-No-more-room... I think you get the idea! Can't remember the last line, but it was the same every time, something like Along/On the road to [pick a destination: scansion suggests a 2-syllable name stressed like Boston/London].

You can sing this to any nursery-rhyme ditty - ours was basically Here-We-Go-Round-The-Mulberry-Bush (itself another candidate) in a slightly different rhythm. Somebody try PM-ing Azizi - she has a treasure-trove of material which may well include some gems for tiny children.