My vote for the most convincing fictional song is ‘That Thing You Do!,’ from the 1996 film of the same name. This track is the one-hit wonder by 60s pop band The Wonders, and it perfectly captures the sound and spirit of that time.
That Thing You Do! (the movie) was the writing and directing debut of Tom Hanks. It’s a charming film that never quite found an audience. It chronicles the short career of a band called The Wonders (renamed from The Oneders after everybody mispronounced it as the O-need-ers) that sends this song up the charts before falling apart.
The song was written by the late Adam Schlesinger of Fountains of Wayne, one of our great modern pop tunesmiths. It made it to #41 on the Billboard Hot 100 and was nominated for an Oscar and a Golden Globe (losing both to ‘You Must Love Me’ from Evita).
Hanks didn’t write and direct another film until 2011’s Larry Crowne, a considerably less successful project than this one.
You
Doing that thing you do
Breaking my heart into a million pieces
Like you always do
And you
Don’t mean to be cruel
You never even knew about the heartache
I’ve been going through
[Chorus]
Well, I try and try to forget you, girl
But it’s just so hard to do
Every time you do that thing you do
[Verse 2]
I know all the games you play
And I’m gonna find a way to let you know that
You’ll be mine someday
‘Cause we
Could be happy, can’t you see?
If you’d only let me be the one to hold you
And keep you here with me
[Chprus]
‘Cause I try and try to forget you, girl
But it’s just so hard to do
Every time you do that thing you do
[Bridge]
I don’t ask a lot, girl (I don’t ask a lot, girl)
But I know one thing’s for sure (know one thing’s for sure)
It’s the love I haven’t got, girl
And I just can’t take it anymore
[Verse 2]
‘Cause we
Could be happy, can’t you see?
If you’d only let me be the one to hold you
And keep you here with me
‘Cause it hurts me so just to see you go
Around with someone new
[Outro]
And if I know you, you’re doing that thing
Every day just doing that thing
I can’t take you doing that thing you do
Meet Me In Montauk 
Love this movie, and the song should have won the Oscar!
I remember the film but not sure I ever watched it. Always love Tom Hanks and he is a very talented writer. I’ve read his short stories