You're right, there aren't many:

24 Hours from Tulsa.

From Clare to Here (well, it's a different kind of desertion maybe)

Down in the Sally Gardens (But that's more regrets rather than remorse.)

But that's all I can think of, and only one of them fits the bill, and that's by a long way the least of the songs.

I once wrote a song with the rather lengthy chorus:

So he lied through his teeth
and that's the living proof
that he loved her too much
to always tell the truth.
He loved her too much to never tell a lie
and that's the reason why at times
he used to look her in the eye:
"I'll swear once again, the way I always do,
I'd never tell a lie to you.
Would I ever tell a lie to you,
have I ever told a lie to you?"

But that's more an excuse song, as is "You always hurt the one you love."