Here's a more coherent version, from the Old-Time String Band Songbook (Oak Publications). No songwriter listed, so maybe it is "traditional." Basically the same words as Murdock has.
-Joe Offer-

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A Dollar Down and a Dollar a Week

A friend of mine bought a radio,
For a dollar down and a dollar a week;
Says he, It's the easiest trap I know,
A dollar down and a dollar a week.

So he bought a rug and a fountain pen,
A run-about car out here and then
A set of the lives of the famous men
For a dollar down and a dollar a week.

Then he bought a suit and a hat and shoes
For a dollar down and a dollar a week,
Joined the lodge and paid his dues,
Was a dollar down and a dollar a week.

And he bought a ring that was fair to see
For the lily-white hand of his bride-to-be;
When he got married, the minister's fee
Was a dollar down and a dollar a week,

When the baby came, the doctor got
A dollar down and a dollar a week,
My friend he clothed and fed that tot
With a dollar down and a dollar a week.

At last said his wife, "I must be free,
These weekly payments are ruining me
She got a divorce and the alimony
Was a dollar down and a dollar a week.

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Click to play

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Not much in the Traditional Ballad Index, other than what's in the Old-Time Stringband book:

Dollar Down and a Dollar a Week

DESCRIPTION: Singer describes all the things his friend has bought on credit, including clothes, car, marriage, and a child; finally the man's wife, saying "these weekly payments are killing me," divorces him, and the alimony is a dollar down, a dollar a week.
AUTHOR: unknown
EARLIEST DATE: 1931 (recording, Arkansas Woodchopper)
KEYWORDS: marriage money humorous commerce
FOUND IN: US(SE)
REFERENCES (1 citation):
Cohen/Seeger/Wood, p. 79, "Dollar Down and a Dollar a Week" (1 text, 1 tune)
RECORDINGS:
Arkansas Woodchopper [pseud. for Luther Ossenbrink], "A Dollar Down and a Dollar a Week" (Conqueror 7887, 1931)
Woody Guthrie & Cisco Houston, "A Dollar Down and a Dollar a Week" (on Struggle2)
CROSS-REFERENCES:
cf. "Cotton Mill Colic" (theme)
Notes: And this was before Visa cards even existed.... - RBW
File: CSW079

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The Ballad Index Copyright 2008 by Robert B. Waltz and David G. Engle.

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Roud (click) refers only to the Woody Guthrie recording.