Douglas Harper's Etymology Dictionary
1913 (from 1912 as a noun), said to be carnival slang and imitative of the sound of banjo music at parades [Barnhart]; compare ricky-tick "old-fashioned jazz" (1938). But early records suggest otherwise unless there are two words. The earliest senses seem to be as a noun, "maltreatment," especially robbery:\n\nSo I felt and saw that I was robbed and I went to look after an officer. I found an officer on the corner of Twenty-fifth street and Sixth avenue. I said, "Officer, I have got the rinky-dink." He knew what it meant all right. He said, "Where? Down at that wench house?" I said, "I guess that is right."
[testimony dated New York August 9, 1899, published 1900]
\nAnd this chorus from the "Yale Literary Magazine," Feb. 1896:\nRinky dinky, rinky dink,\nStand him up for another drink.\n
Wiktionary
a. (context informal English) Of poor or inferior quality; hokey; sloppy; chintzy; small; flimsy; inadequate.
Usage examples of "rinky-dink".
My intention was to reach a position far enough from Kedge-Lockaby so that I would not disrupt electromagnetic systems on its surface when I made my hyperspatial leap, yet close enough to the planet so that it would eclipse the dazzling EM pulse of my ultraluminal crossover from the rinky-dink sensors of the tender.
I say to Cleo, "but so far you've had exactly one hit single for a rinky-dink label.
Well, try to imagine, if you will, a country without neon signs, McDonald's, or corner gas stations, a country where suburb doesn't mean PTAs and lawn mowers but means a shithole village close enough to a rinky-dink city to have a few buildings with glass windows and no pigs in the street.