I corresponded with a lovely young man named Ben Belzer last year, and he had this to say:

Hi, Daphne,
I was recently looking for the lyrics to Surabaya Johnny on
the internet, and, although I had no luck, I do know that
the song is from the play "Happy End" by Bertold Brecht, and
that it was written by Kurt Weill.  The song is in German
and I have a sneaking suspicion that if you call your local
library, they may have a copy of the play (and maybe the
song lyrics).
Let me know if you have any luck.

-Ben

And a second message from Ben, after I'd been busy for a few weeks and not able to reply to mail:

Hi, Daphne,
Well, I hadn't heard if you'd been able to track down the lyrics to "Surabaya Johnny", so I did a little investigating in my local library and found the "English version".  I wasn't able to find the original German version, but here goes...

I had just turned 16 that season
when you came up from Burma to stay
And you told me I ought to travel with you,
You were sure it would be o-kay
When I asked how you earned your living
I can still hear what you said to me:
You had some kind of job with the railway,
and had nothing to do with the sea.

You said a lot, Johnny,
all one big lie, Johnny.
You cheated me blind, Johnny,
from the minute we met.
I hate you so, Johnny
when you stand there grinning, Johnny
Take that damn pipe out of your mouth, you rat!

Surabaya Johnny,
no one's meaner than you.
Surabaya Johnny,
my god, and I still love you so!
Surabaya Johnny,
Why'm I feeling so blue?
You have no heart, Johnny,
and I still love you so!

At the start ev'ryday was Sunday,
'til we went on our way one fine night.
And before two more weeks were over
you thought nothing I did was right.
So we trekked up and down through the Punjab
from the source of the river to the sea:
When I look at my face in the mirror
there's an old woman staring back at me.

You didn't want love, Johnny
you wanted cash, Johnny
but I saw your lips, Johnny
and that was that.
You wanted it all, Johnny
I gave you more, Johnny.
Take that damn pipe out of your mouth, you rat!

Surabaya Johnny,
no one's meaner than you.
Surabaya Johnny,
my god, and I still love you so!
Surabaya Johnny,
why'm I feeling so blue?
You have no heart Johnny,
and I still love you so!

I would never have thought of asking
where you got that peculiar name,
but from one end of the coast to the other
you were known everywhere we came.
And one day in a two-bit flop house
I'll wake up to the roar of the sea,
and you'll leave without one word of warning
on the ship waiting down at the quay.

You have no heart, Johnny
you're just a louse, Johnny.
How can you go, Johnny,
and leave me flat?
You're still my love, Johnny
like the day we met, Johnny
Take that damn pipe out of your mouth, you rat!

Surabaya Johnny,
no one's meaner than you.
Surabaya Johnny
my god, and I still love you so!
Surabaya Johnny,
Why'm I feeling so blue?
You have no heart, Johnny,
and I still love you so!