Ewan,There is a great book of Belfast childrens songs, (quite a few of the street games variety), I'm sure many of them would have been in Scotland too. I remember being sung to sleep with Coulter's candy,..... definately Scottish.
The book is "Keep the Kettle Boiling, Rhymes from a Belfast childhood." by Maggi Kerr Peirce, published by Appletree Press 1983, (ISBN 0-86281-116-3).
Slainte
alison