The card has generally been attributed to 1969 (PSA's choice) and in some cases 1970. However, a little sleuthing revealed those years are both, in fact, incorrect.
I found a blurb from the July 8, 1983 issue of Sports Collectors Digest that offered a couple of tantalizing, albeit fairly non-specific, clues:
OK, seemingly vague and hopeless but if you input "Kuhn" + "Newark" + "Saints" + "Sinners" + "Dinner" into newspapers.com, you get a nice result:
That is from The News of Paterson, New Jersey and the article was in their December 29, 1970 issue. On January 26, 1971 Commissioner Kuhn was honored at the Robert Treat Hotel (now a Best Western) and that is indeed the date of "issue". I've seen estimates of between 100 and 300 copies of this thin card (almost paper, really) being produced and when I checked the capacity of the hotel's ballroom I found a maximum of 1,500. However, it looks like the current ballroom could be a later addition to the hotel; and I suspect the 1971 version held fewer people.
No matter how big the ballroom was, these are difficult, although not impossible, to find. The date however, was not.