My mother's version was longer:-

Christmas is coming
The goose is getting fat
Please put a penny in the old man's hat?
If you haven't got a penny
A ha'penny will do
If you haven't got a ha'penny
A farthing will do,
If you haven't got a farthing a shoe(sic) will do
If you haven't got a shoe, God Bless You!

My suspicion is that "shoe" was origianlly "sou".
This was from Watchet in Somerset.

Robin Madge