What about "I've Got A Crush On You" by Linda Ronstadt? It's on her "What's New" album (1983), which was recorded with the Nelson Riddle Orchestra. It was written by George & Ira Gershwin and has a real 1930s/40s feel to it.
Admittedly, the lyrics here are to be sung by a female, but I HAVE heard a recorded version by a male - the Australian music theatre artist, Anthony Warlow. The male version of the lyrics are shown in red and in brackets.
(Anthony Warlow's versions are on his "Back In The Swing" and "The Best Of Act One" albums.)
How glad the many millions
Of Toms and Dicks and Williams ( of Annabelles and Lillians )
Would be
To capture me
But you had such persistence
You wore down my resistance
I fell
And it was swell
You're my big and brave and handsome Romeo (I'm your big and brave and handsome Romeo )
How I won you I will never never know
It's not that you're attractive (It's not that I'm attractive)
But oh my heart grew active
When you came into view
I've got a crush on you, sweetie pie
All the day and nighttime, hear me sigh
I never had the least notion
That I could fall with so much emotion
Could you coo
Could you care
For a cunning cottage we could share
The world will pardon my mush
Cause I've got a crush, my baby, on you
Could you coo
Could you care
For a cunning cottage we could share
The world will pardon my mush
Cause I have got a crush,
My baby, on you
I guess it depends on whether you want something on the mushy side, or with a bit more of a beat. This one definitely falls into the slow-and-gentle category!
Judy