This can't compete with Rogerbob's entry, but maybe it will give someone else some ideas. Or at least chuckles. Since we're allowed to change the tune for this one, I thought I'd give that a try:
SING, GIRL, DON'T CRY
Sung to the tune of "Big Girls Don't Cry," written by Bob Gaudio and Bob Crewe,
performed by Frankie Valli and the Four Seasons.
INTRO:
Sing, girl, don't cry
Sing, girl, don't cry
REFRAIN:
Sing, girl
Don't cry-ay-ay
(Sing, don't cry)
You're my
Lovely sky
(You're like a lovely sky)
Singing, girl,
Hearts get high-ay-ay
(Hearts get high)
You're my
Lovely sky
(My lovely sky)
VERSE 1:
(Oh, those eyes)
Down the hairpin mountain track
(Oh, those eyes)
Lurk a pair of scouts in black
(Oh, those eyes)
Like a highwayman's attack
Sing, girl, don't cry
REFRAIN
VERSE 2:
(Just one hug)
Since you are the girl next door
(Just one hug)
Just a step away, no more
(Just one hug)
One caress I'm asking for
Sing, girl, don't cry
REFRAIN
VERSE 3:
(Mine, all mine)
Near your mouth, that mole you've got
(Mine, all mine)
Don't you dare give up that dot
(Mine, all mine)
It belongs to me, that spot
Sing, girl, don't cry
REFRAIN
VERSE 4:
(Silly bird)
Any bird, when it has strayed
(Silly bird)
Finds its nest has been re-laid
(Silly bird)
Serves it right, it should have stayed
Sing, girl, don't cry
REFRAIN
[And yes, I'm aware that "Lovely sky" is a really lousy and unidiomatic translation of "Cielito lindo."]