I tried and failed, too.

Searching under "little boy" plus 'shoes' and a few other things didn't yield much.

Then I wondered whether your lyrics were correct, and searched more generally. I got this (it isn't what you're looking for):

"LITTLE BOY BLUE
Eugene Field



The little toy dog is covered with dust,
But sturdy and staunch he stands;
And the little tin soldier is red with rust,
and his musket moulds in his hands.
Time was when the little toy dog was new,
And the soldier was passing fair;
And that was the time when our Little Boy Blue
Kissed them and put them there.



"Now don't you go till I come.", he said.
"And don't you make any noise!"
So, toddling off to his trundle bed,
He dreamt of the pretty toys;
And, as he was dreaming, an angel song
Awakened our Little Boy Blue.
Oh! the years are many, the years are long,
But the little toys friends are true.



Ay, faithful to Little Boy Blue the stand,
Each in the same old place,
Awaiting the touch of a little hand,
The smile of a little face;
And the wonder, as waiting the long years through
In the dust of that little chair,
What has become of our Little Boy Blue,"

..and lots of hits about the boy blue who blows his horn.

Are your lyrics exactly, precisely correct? And do you know who wrote the song?

There's a search engine I used once upon a time that included so much information that it actually included our posts on AWAD. No joke. If I could remember that search engine, it might have the lyrics.

"The Little Boy with Two Little Shoes" -- entered just that way -- gets nada.