My transcription from a recording on Spotify:

YE CAN COME AND SEE THE BABY
As sung by Will Fyffe

1. Oh, the wife and I felt very, very lonely for a while,
Sittin' in the kitchen by oorselves,
Till one day over tea, the wife she told tae me
A secret that I couldnae keep mysel;
So at three o'clock this mornin', I wis runnin' doon the street.
The neebours must 'a' thought there was a fire.
The polisman was laughin' lood when I came back again,
For by ma side was Doctor McIntyre.

CHORUS: An' you can come an' see the baby any day ye care to call.
He's lyin' by his mammy in a wee white shawl.
He looks so cute an' slanky like a dumplin' in a hankie,
An' we're goin' ta call him William Angus Jamieson Jock McCall.
Tirra madee madoo maday, tirra madee madaddy-o.
Tirra madee madoo maday. I am his daddy-o.

2. Mind you, I'm a chap that very, very seldom takes a dram.
In fact, it's very seldom in the hoose,
But today I feel so glad that I've been made a dad,
I'm entitled for to go upon the loose.
So since op'nin' time this mornin, I've been treatin' all ma pals,
For they said that I must wet the baby's head.
Man, I felt a priggly(?) chap when they slapped me on the back,
So I waited until closing time and said: CHORUS