When I was child up in northern Wisconsin, my grandmother had record with with watermelon smiling on on the vine on it. It was completely different though from the lyrics other people have posted. The song as I know it goes like this.

Watermelon smiling on the vine
It's summertime and watermelons fine
It's red in the middle and green on top
Makes your tounge go flippity flop

Old farmer Grey has gone away
And I know that his melons are sweeter than the hay
I hop rightover and get me one
Hear a shot and away I run

Watermelon smiling on the vine
It's summer time and watermelon's fine
Their white on the bottom and red in the middle
Sweeter than a tune on a fiddle

This is all I can remember, since it has been over 75 years since I heard this song.