Johnathan's words about "eeney, meeney" sent me off on an internet toot, the result being the discovery of a web page with possibly all of the Waterson's song lyrics at Watersons
For textophiles, thats http://hum2mac1.murdoch.edu.au/watersons/links.html

The counting song I was looking for is The Lincolnshire Shepherd at this place
http://hum2mac1.murdoch.edu.au/watersons/lincolnshire.html

Yan, tan, tethera, tethera, pethera, pimp.
Yon owd yowe's far-welted, and this yowe's got a limp
Sethera, methera, hovera, and covera up to dik,
Aye, we can deal wi' 'em all, and wheer's me crook and stick?