Question

Are there any songs with internal rhyme in the lyrics?

Answer 1

Lots of popular songs use internal rhyme.
(See below for an example)

Explanation:

select lines from "Don't Stop Believing"

A singer in a smoky room, the smell of wine and cheap perfume

Working hard to get my fill, everybody wants a thrill

Some will win, some will lose, some were born to sing the blues

(for a more traditional song)
selected lines from "Oh My Darling Clementine

Near a cavern, across from a canyon,
Excavating for a mine,
Lived a miner, forty-niner
And his daughter Clementine

How i missed her, how i missed her, how i missed my Clementine!
Til' i kissed her little sister, and forgot my Clementine.

or...
selected lines from the Beatles "Hard Day's Night

It's been a hard day's night, and I'd been working like a dog
It's been a hard day's night, I should be sleeping like a log
But when I get home to you I find the things that you do
Will make me feel alright.