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.