A few comments.

1. There is a song called something like "A donkey cart made for two", starting Sarah, Sarah, which seems to predate "Daisy Daisy" and her bicycle, and also Daisy Bell. I will try and dig it out from the Bodleian, where I found it.

2. "They dug up Billy's bones to make a sewer" might be derived from, or related to "They're moving Grandpa's grave to build a sewer"

3. Yes, it did remind me of Lizzie Borden too