The 1989 movie takes place in an alternate 1979, based on the American Express Card advertisement reference and dates on props. The sequel, Batman Returns can take place no further back than 1983, based on the Love Connection reference and Penguin's birth certificate prop. It's interesting that both dates are pretty much exactly a decade prior to the real-world release years. The prop people/script supervisor/director must have been proceeding on agreement to this rounded off timeline.

While an actual Penguin birth certificate exists, I can't find it in the film. I can see other birth certificates, however, and they do say 1950-1951.

Batman has dates stating 1913, 1947, 1948 and 1953. I saw someone place the Burton films in 2013 and 2016, I think, based on Jack Napier's criminal record. The Catwoman 80th Anniversary story featuring Michelle Pfeiffer is stated as the 1940s Catwoman.

Unfortunately, I don't think they paid attention to the timeline that closely.

I'm aware of 90% of the newspaper props and wanted poster being mostly gibberish, since they never expected anyone to ever look at it that closely. Of course those random small props offer contradictions. But my main point is references to pop culture in our world, spoken as lines of dialogue in the film would be "a-level" canon that can't be swept under the rug like everything else. And there are major visual props that have large print, knowing that the audience could spot it. (the date Shreck's company was founded on side of a loading truck) Shreck seems older than the other characters, only slightly younger than Grissom. And the birth certificate seems like thought was put into it, mores so than the newspapers. Even though chose not to show it, it's still production made and i'd put it above the average newspaper prop. The villains whole plot and motivation revolves from birth certificate research scene and his mysterious list.

Terrible expanded universe comics never make any sense. Has nothing to do with the actual movie.

I agree that the series isn't set in the 1940s. Seemed half-assed, especially when that comic had modern computers, likely a consequence of this universe having a different technological development timeline than the real world. The comic isn't bad, but it does feature a Penguin cameo that clearly isn't Danny DeVito or a corpse, so I guess, just like Joker, a successor/copycat continues the name.

Could you explain each piece of evidence for each film's timeline? I would find it very useful. Is Penguin's birth certificate ever in the film and I just missed it?

I don't remember it being there. I do think, however, it's just an alt-history, kind of like Watchmen or X-Men