There's another thread (from 11 years ago) about this song, here: So sing a song, a drinking song.

It gives a bit more, but it's incomplete, according to the person who posted it::

Of all the songs, I'd like to sing
A drinking song's the best, sir,
And with my pint pot in my hand
I'll put it to the test, sir.

CHORUS: So sing a song, a drinking song
And sing it just for pleasure
And when that song be o'er and done
We'll have another measure.