Tay Bridge is Broken and I'm come to mend it, The

A children's game song. 

This presumably evolved some time after the disaster; but given the nature of children, not necessarily very long.

The Folktrax website gives "The Tay Bridge is broken and I'm come to mend it - fal the doo a dido" and says that it is a children's game.

http://folktrax-archive.org/menus/search%20for%20titles_ta_tcha.htm