(Thanks for just asking for sources rather than immediately attacking the intensions of the grandparent.)
So a couple of Google searches show that there are dozens, maybe hundreds, of online lists of failed predictions of climate change maintained by climate change skeptics. For instance:
https://www.thenewamerican.com/tech/environment/item/18888-e...
From that list, I picked one story to track down:
> On June 30, 1989, the Associated Press ran an article headlined: “UN Official Predicts Disaster, Says Greenhouse Effect Could Wipe Some Nations Off Map.” In the piece, the director of the UNEP’s New York office was quoted as claiming that “entire nations could be wiped off the face of the earth by rising sea levels if global warming is not reversed by the year 2000.” He also predicted “coastal flooding and crop failures” that “would create an exodus of ‘eco-refugees,’ threatening political chaos.”
Worryingly, searching for this headline mostly returned more climate change skeptics websites. But this isn't totally unexpected since it dates to before internet adoption, and I was eventually able to find this archive photo from a local newspaper that appears to substantiate it.
https://www.newspapers.com/newspage/83413062/
Thats just sample size 1, though. Will see if I can find a NYTimes article.
Edit: So a lot of these lists look like copypasta. Some are partial, but here is a pretty complete version:
http://forum.weatherzone.com.au/ubbthreads.php/topics/109996...
There are several mentions of the NY Times, and the two I checked were real (including at least one which was just a letter to the editor, and so not endorsed by the paper.) Note that these predictions are generally for global cooling. Many people says it's unfair to quote these claims because they did not represent the consensus position at the time (but this doesn't invalidate the grandparent's claim; he doesn't say NY Times).
Anyhow, I would love to someone else take this further, but my initial impression is that the claim "there were a bunch of plausible sounding stories about coastal flooding in reputable newspapers" is probably true, but that this doesn't mean it reflected a consensus view back then. On the other hand, the current story also doesn't reflect a consensus view regarding any near- or medium-term claims.