This one is called Lúrabóg, Lárabóg or Lúrapóg, Lárapóg. Apparently there must have been quite a few variations of it. On the Duchas website it's described as a game, apparently for adults, where they are sitting before the fire, legs outstretched and someone has a stick, and as he recites the rhyme they have to draw in their legs and last one gets hit on the foot. It's also described as a children's guessing game. This is the text I have noted down, but I can't remember where it comes from.

Lúrabóg, Lárabóg

Buí Ó Néill
Néill an plobán
Plobán súlach
Súil na seicne
Seic na meilleach (I'm not sure what this means)
Ál na gcoileach
Súistín, buailtín (súistín = saoisteog, which can mean a soft low seat made of rushes or of plaited straw or a dumpy, little woman) buailtín can also be variant of buailteán
Maidí beaga peicín
Buille beag ar bharr na croise
'S crap isteach an fhideog. (fideog = feadóg - but apart from a whistle, would this mean a leg ?)

There's seem to be quite a lot of hidden meanings here, does anyone understand them?

There are version on the Duggans' CD Rubicon as well as on the CD Gugalaí Gug

On the Duchas.ie website (the 1937 Schools Project) the version they have there is -

Lúrabog, larabog
Líam Ó Néill
Seághan Ó Plubán
Plubán seichne, seichne (lán) mille
Lán plubán cuir i g-clais é