An Elephind newspaper database search turns up one very lonely instance of "junk bonds" from more than one hundred years ago, in the San Francisco [California] Call (October 24, 1911):
'JUNK BONDS' MAY BE WORTH $800,000
Mexico Will Be Asked to Redeem Old Documents Hauled Out of a Trunk
Believing that Mexican government bonds and securities, which 32 years ago were declared worthless, can be converted into cash to the amount of $800,000, David Craelius of Mill Valley yesterday applied for special letters of administration in the estate of Charles J. Janson, who died in this city in 1879.
Judge Coffey, before whom the application was brought, granted Craelius' petition and placed him under bonds in the nominal sum of $1,000.
When the will of Charles J. Janson was filed in 1879 the widow, Mrs. Therese Louise Janson was appointed executrix. The bonds and securities, which Janson had received during turbulent times in Mexico were among the personal effects left. Investigation indicated that they were without value. The estate was divided and the stocks and bonds thrown into a trunk and forgotten.
Recently Mrs. Janson mentioned that, she still had possession of the documents. Her son in law, Craelius, became interested, and after consultation with his attorney, Rufus C. Thayer, it was decided that he should endeavor to convert the bonds into cash.
In this extreme chronological outlier, "junk bonds" means "bonds tossed into a trunk after being deemed worthless." There seems to be no line of continuous usage between this instance and the instances of "junk bond" that begin to appear in the late 1970s in Elephind search results.
The earliest Elephind match for "junk bonds" in the modern sense of the term appears in the Santa Cruz [California] Sentinel (September 30, 1977), in the form of a brief reference to a TV program called Wall Street Week that was devoting a show to junk bonds:
WALL STREET WEEK "A Junket Into Junk Bonds" Guest: Harry Freeman Jr., Assoc. Managing Partner, Lord, Abbett & Co.
The next mention comes about six months later, in Robert Murick, "Pick the Right Mutual Fund" in the [Palm Springs, California] Desert Sun (March 27, 1978):
"JUNK" Many investors find what is commonly called a junk bond fund to their liking. This type of fund goes in for bonds with low ratings coupled with higher than normal yields. A variation on this theme is the junk municipal bond fund. Here the individual can participate in state and local bonds with low ratings. Like other municipal bonds, they are free from the clutches of the lax collector.
Roughly the same age as these instances is one for "junk stock" in Donald Bauder, "Don't Play Around With Today's Stocks," again in the [Palm Springs, California] Desert Sun (January 22, 1978):
The fun stocks are beginning to look like funk stocks. A funk stock, of course, is not as unappealing as a junk stock in the current market but the similarities are remarkable. The fun stocks are, of course, the leisure-time stocks, including the makers of recreational durable goods (Brunswick, AMF, Outboard Marine, etc.).
From the admittedly narrow array of daily newspapers available for Elephind searches in the 1960s and later, it appears that "junk bond" in its modern sense was in use by late 1977 and that "junk stock" was in use by early 1978.