Not sure if everyone here is aware that there is a group on this site dedicated specifically to Atheist songs with over 100 songs posted (I just checked and was a little dismayed that my post of just over a month ago was the most recent one, so someone better post something there before the Admins kill the group off) [agnostic.com] .

I recommend you get on youtube and watch Father John Misty perform at the Roskilde Festival in Copenhagen in 2017. The first song he sings "Pure Comedy" is a great song and has much to do with atheism. The Coppenhagen kids are ahead of ours, but then all of Europe is as far as progressive thinking and social responsibility go.
Father John Misty (JoshTillman) grew up in Evangelical household in Maryland. He rebelled.

Three songs come to mind-- two are very direct songs by the Dead Kennedys, "Religious Vomit" and "Moral Majority." One of them has the line, "God must be dead if you're such a fool," or something to that effect. Jane's Addiction has "Had a Dad," which includes the line, a slight change from previous iterations of it in the song, to something like, "have the feeling that God is dead."

Here's my offering.

I was going to comment on some songs that were skeptical or irreverent, until I took a look at another page that reminded me of "Heresy" by NIN; "God is dead/And no one cares/If there is a Hell/I'll see you there." That's pretty stark.

Imagine is not an atheist statement as Richard Dawkin's would have you believe.
Let's hear it in Lennon's own words, from a Dec 1980 interview with playboy

The concept of positive prayer ... If you can imagine a world at peace, with no denominations of religion—not without religion but without this my God-is-bigger-than-your-God thing—then it can be true

And here is what he said about himself in a Sept 1980 interview with playboy.

People always got the image I was an anti-Christ or antireligion. I'm not. I'm a most religious fellow. I was brought up a Christian and I only now understand some of the things that Christ was saying in those parables. Because people got hooked on the teacher and missed the message."

Look up a band called Monster on Sunday.

This does not have a huge amount of atheist stuff in (it’s all quite gentle) but it does have this verse which I love:

I don't go in for ancient wisdom
I don't believe just 'cause ideas are tenacious it means they're worthy
I get freaked out by churches
Some of the hymns that they sing have nice chords
But the lyrics are dodgy

And it’s a nice song, Tim Minchin “White Wine in the Sun”

I have an issue with John Lennon.

Here's a curious and very serious song about disbelief from Crosby, Stills and Nash:

Dream Theater has several songs on this topic. My two favorites are "Surrounded" and "Take the Time".

"Faithless" by Rush

Great question.