I've heard and sung this song all my life. The chorus is the same as you show here, but the lyrics are a little different. The version I know is as follows:

Skinnamarinky-dinky-dink!
Skinnamarinky-doo!
I LOVE YOU!

Skinnamarinky-dinky-dink!
Skinnamarinky-doo!
I LOVE YOU!

I love you in the morning
And I love you late at night.
I love you in the evening
When the moon is shining bright.

Ooooh! Skinnamarinky-dinky-dink!
Skinnamarinky-doo!
I LOVE YOU!