With that in mind, here's my transcription of Darby and Tarleton's version (listen). "Air that news" could easily be "hear that news," but it wouldn't make sense for Spaniards to have the news on the city. I also went back and forth on the third line of the chorus; it could have been "San Francisco oughta lie low," but I don't love the "low" part of it. Also a bit unclear on what Uncle Sam says, but I think this is closer than "what makes four winds beat."

BIRMINGHAM
(as recorded by Darby & Tarleton)

I have traveled east and west
Been helped to stop to rest
But I've never seen a town like Birmingham

CHORUS (x2)
Oh, my, she has certainly won the prize
The swiftest little town in Alabam'
San Francisco, what a lala, she lost her bottom dollar
And she'll never beat a town like Birmingham

I have traveled through Albania
Egypt and Australia
I went to see the Mikado of Japan
And the King and Queen of Spain
Invited me to call again
Cause I like to air that news from Birmingham

CHORUS (x2)

I have traveled all around
New York and Alabam'
That is the jewel of Uncle Sam
These words he had to say
"Don't you give this town away"
Said, "What makes for all I feel is Birmingham"

CHORUS

Don't believe what I say is true
I'll tell you what you do
I'll send it to a friend that's always right
He would tell you in a minute
San Francisco, she ain't in it
But old Birmingham is certainly out of sight

CHORUS

I've traveled east and west
Watched the sun to rest
But I've never seen a town like Birmingham