I did a bit more research. A good tip for researching labels is to google the exact text of the label in quotes. You will then usually find other examples of the label, and possibly sites discussing the label.
So by
googling: "do not use petroleum solvents or the coin operated method of dry cleaning" I found:
There are several news paper articles from early 1972 discussing the then new care labelling requirements. In July 1972, care labelling became mandatory for new garments in the USA. In the guidance given to manufacturers from the Federal Trade Commission, this exact text was given as an example of an acceptable label. See
here.
Dry cleaners were not happy about this wording, as most dry cleaning was
either petroleum solvent
or coin op, and so the label ruled out most available dry cleaning methods. So later that year, the authorities changed the suggested wording to simply "Dry Clean Only" (see
Family Ecnomics Review, published 1973)
This doesn't mean that such labels were only used in 1972 - and certainly they are later examples, into the 1980s. But it does means that a quantity of labels with this wording would have been made up in 1972, to meet the new 1972 labelling requirements. Also probably not many such labels were made after 1972, as the guidelines had changed. As with other labels, manufacturers probably had stocks of them that they used up, after the guidelines changed.
Whether this wording existing on labels before the 1972 guidelines, who can say - it quite possible some manufacturers already used that wording, and that's where the authorities got the wording from. But to me the likelihood is that it's post 1972.
I also found several examples of garments with that labelling, and none were earlier than 1970s.