Greengal,

This song is usually titled "down By The Bay". I'm not sure where it comes.

Here's two online references to it:

Wikepedia:

"Down by the Bay" is a traditional children's song. A famous version was performed by Raffi and Randy Luxton.

The song lyrics usually are as follows:

Down By the Bay

Down by the bay (repeat),
Where the watermelons grow (repeat),
Back to my home (repeat),
I dare not go (repeat),
For if I do (repeat),
My mother will say:"
Usually follows some kind of variation on "Did you ever see a _____, _____ing a _____", with rhyming words, for example:

"Did you ever see a goose, kissing a moose?"
"Did you ever see an ant, eating a plant?"
"Did you ever see a whale, with a polka-dot tail?" (this is the original variation)
"Did you ever see a bear, combing his hair?"
"Did you ever see a llama, eating his pajamas?"
"Did you ever see a fly, wearing a tie?"
"Did you ever see a bee with a sunburned knee?"
"Did you ever have a time when you couldn't make a rhyme?"
"Did you ever see a rhino kissing a dino?" (Barney and Friends)
"Did you ever see a goat standing in a boat?"
"Did you ever wonder why, I've always sounded high?"
..."Down by the bay."

http://en.wikipedia.org/wiki/Down_by_the_Bay

-snip-

kididdles:

"Down By the Bay

Written By: Unknown
Copyright Unknown

Down by the bay
Where the watermelons grow
Back to my home
I dare not go
For if I do
My mother will say
"Did you ever see a bear
Combing his hair
Down by the bay?"

Down by the bay
Where the watermelons grow
Back to my home
I dare not go
For if I do
My mother will say
"Did you ever see a bee
With a sunburned knee
Down by the bay?"

Down by the bay
Where the watermelons grow
Back to my home
I dare not go
For if I do
My mother will say
"Did you ever see a moose
Kissing a goose
Down by the bay?"

Down by the bay
Where the watermelons grow
Back to my home
I dare not go
For if I do
My mother will say
"Did you ever see a whale
With a polka dot tail
Down by the bay?"

http://www.kididdles.com/lyrics/d007.html