No, I'm not talking about Christian rock or undiluted gospel. Something about searching for the meaning of life, and in particular wanting to connect with the supernatural -- not "finding yourself" by landing the right study-abroad program or scoring the perfect unpaid summer internship.
My hunch is that this kind of music will soar in production and popularity when the violence level is shooting up, because that's when people get more curious about the spiritual, the supernatural, the mythological, the religious... whatever you want to call it. Especially during the second half of the climb in the crime rate, since that's when things start to look apocalyptic -- there's already been half a generation or more of steadily worsening security, and the experts have thrown every social engineering program at it, yet come up with nothing powerful. For similar reasons, it will not tend to adhere to orthodox religion but be less clearly defined, since the failure of the old ways means they must try to figure it out as they go along.
Probably the best example is a #1 hit from 1986, "Higher Love" by Steve Winwood. It couldn't have been made in 1966 because society had only gone somewhat outta whack by that point -- the decay of order got a lot worse in the next 20 years. Typical of an end-times yearning for community, he levels distinctions that exist in the ordinary, falling-apart world by giving it a heavily African sound for white pop music, and I'll bet a lot of people listening to it thought he was black.
Real Life made "Send Me an Angel" in 1983, which is Pagan in tone, and whose video has a pre-Christian but still Indo-European religious feel. Toward the tail-end of wild times (1990) they released "God Tonight", which sounds like the thoughts of a cult leader mixed in with a good dance track.
Belinda Carlisle's "Heaven is a Place on Earth" from 1987 is a bit more focused on the profane than the others, but its power still depends on the desire to bring the supernatural realm down onto our own. Again shades of cult / commune-like concepts of ushering in paradise in this world, although more of the naive free love type than the apocalyptic type.
Of course there was Madonna's last great hit, 1989's "Like a Prayer". The phrases "I want to take you there" and "in the midnight hour" hint at going to some other plane of existence.
"I Still Haven't Found What I'm Looking For" by U2 in 1987 has a nice line that highlights the leveling of distinctions when the end comes: "I believe in the Kingdom Come / Then all the colors will bleed into one."
Camper Van Beethoven's "She Divines Water" from 1988 shows that even college rock, typically not religious at all, could put out a catchy song with an other-worldly feel. Probably the most imaginative and original one of the bunch here.
The 1986 soundtrack for Labyrinth features David Bowie calling all the misfits of the world into joining his utopian cult in "Underground," which has a gospel section later in the song.
"Personal Jesus" from 1990 by Depeche Mode is about a lost soul seeking communion with the divine, although told not from their point-of-view. "Reach out and touch faith" means that the supernatural has become tangible.
There are other songs that are quasi-religious but that do not stress the meeting of the natural and the supernatural. "Man in the Mirror" by Michael Jackson from 1987 is a straightforward conversion-of-the-rich-miser story. Although more difficult to interpret religiously, Madonna's 1984 hit "Like a Virgin" has that "I was lost but now am found" theme, and her conversion sounds like it sprang from some magical rather than mundane cause. In 1981 Orchestral Manoeuvres in the Dark made not one but two hagiographic songs about the same saint -- "Joan of Arc" and "Maid of Orleans". The song and album "1999" by Prince from 1982 is apocalyptic, but his response is to retreat into a not very sacred kind of hedonism.
Nothing else in the yearning-for-the-supernatural genre comes to mind, although I could be missing some stuff from the later part of the '70s, when cults and evangelism were ramping up in popularity compared to the '60s. I'm pretty sure there's little or none from the '60s and earlier '70s, nor from the early '90s through today. And during the previous period of falling crime, the mid-'30s through the late '50s, the hit songs featured more trivial subject matter and a secular frame-of-mind, however catchy it may or may not sound (Frank Sinatra, Ella Fitzgerald, Bobby Darin, etc.).