Projecting backwards is difficult, of course, but I think that many songs could do well (if not necessarily be chart toppers) in a lot of time periods. The main criteria I see are:
- It’s fun to sing.
- Its lyrics are not explicitly and extensively tied to events of its native period.
- It’s not too raucous instrumentally.
- Its lyrics are not such as would prevent the song’s performance.
I think you could make a case for “Tainted Love”, “Sweet Dreams”, “Eye of the Tiger”, and many other songs. Strong beats, non-specific but identifiable lyrics, nothing too out there melodically.
Going the other way–songs from prior eras being popular now–we potentially have some interesting data available now, courtesy of video games. A number of games have done well musically by incorporating songs from past eras or by retrofying modern songs. The popularity of the results suggests that there’s a modern popular market for those songs.
Consider Fallout 3. The intro song to the game is “I Don’t Want to Set the World on Fire”, released by the Ink Spots in 1941. It’s very, very different from modern pop, yet the top YouTube listing for it was posted 6 years ago, and it has over 5 million hits. One of the more popular mods for the game adds about 100 more period songs. Not all of them could stand on their own as a release, of course, but I’m sure some would make the cut.
Bioshock: Infinite went a different route. It took modern (or at least more recent songs) and created period covers of them in various styles, like “Fortunate Son” as a spiritual–which, for a measure of modern popularity, has nearly 400k hits on YouTube. Scott Bradlee’s Postmodern Jukebox, the group that did many of the other covers, has nearly 2 million subscribers. Again, I think this demonstrates that there is a modern audience for songs in these styles.
I suspect that the biggest limiting factor is getting them played and promoted. Currently, people get exposed to them incidentally, rather than through their music-specific channels. There’s not much push behind them–but that isn’t as crucial as it used to be. People are more free now to pick and choose the music that suits them than they have ever been, and it’s starting to show.