This was mentioned by Musicman on 21 Nov 98 - 03:39 AM. From the sheet music at Mississippi State University:


LET A SMILE BE YOUR UMBRELLA (ON A RAINY DAY)
Words by Irving Kahal and Francis Wheeler; music by Sammy Fain, ©1927.

1. Once I met a happy little bluebird.
I was just as blue as could be.
In a little while,
I began to smile,
When he sang this merry song to me:

CHORUS: “Just let a smile be your umbrella on a rainy, rainy day;
And if your sweetie cries, just tell her that a smile will always pay.
Whenever skies are gray, don’t worry or fret.
A smile will bring the sunshine and you’ll never get wet.
So let a smile be your umbrella on a rainy, rainy day.”

2. As I listened to that happy bluebird,
I soon learned his smart philosophy.
On my window sill,
He began to trill.
This is what he had to say to me: CHORUS

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There are tons of recordings on the Internet Archive. Many of them are instrumentals, or they sing only the chorus. These are the ones that sing at least one verse:

Singer and Morton, on Oriole (1137 (a)), 1927. They sing the chorus, verse 1, chorus, bridge, chorus. This bridge does not appear in the sheet music:

Remember that a cheerful smile is always bound to win,
So never pull the shades down when the sun wants to come in.
A smile is just a slicker and it’s always still the line(?),
And if you wear it, you are sure to find
That ev’ry raindrop soon becomes a little pearl of joy,
And you’ll keep going along just like a whistling barefoot boy,
So pack up all your troubles in a great big pile (or “pipe”?) of bubbles,
And blow, blow, blow them all away

Dolly Kay and the University Six, on Diva (2581-G), 1928. She sings the first verse, chorus, bridge, plus this alternate chorus which is not in the sheet music:

Just let a smile be your umbrella on a rainy, rainy, ray-ray-rainy day.
Just pucker up your lips and whistle and your blues will pass away.
For never let your friends see you wear a frown,
’Cause one by one they’ll walk away and all turn you down,
So let a smile be your umbrella on a rainy, rainy day.

Jay C. Flippen and His Gang on Perfect (12406), 1928. He sings the first verse and chorus, plus the following alternate chorus:

Just let a smile be your umbrella on a rainy, rainy day.
Just pucker up your lips and yell a great big “Hip-hip-hip-hooray!”
Grab all your cares and pull them out by the roots.
Just wear a smile and throw away those old rubber boots
And let a smile be your umbrella on a rainy, rainy day.

Lee Morse and Her Blue Grass Boys, on Columbia (1303-D), 1928. She sings the first verse, chorus, second verse, second chorus, alternate chorus, as above.)