Sheree, I am familiar with a version of the first rhyme you posted.

That rhyme provides commentary on race in America-both from the viewpoint of White America, and also with regards to inracial color preferences among African Americans.

Here's the version of that rhyme that I know:

If you're white you're alright
if you're brown stick around
if you're black get back.

Demographical information: recited & heard in Atlantic City, New Jersey {mid 1960s and possibly before that}, and in Pittsburgh, PA {late 1960s to date}.

Note that we didn't have the part about if you're yellow or if your red...

I remember reciting this rhyme as a young child, probably while jumping rope:
Yellow yellow kiss a fellow
Red red pee the bed
White white say goodnight.

-snip-

If the "Yellow yellow" rhyme had anything to do with race, I don't think the kids reciting it knew it. Personally, I'm not convinced that rhyme. In contrast, the "If you're White" rhyme was recited by Black teens and Black adults who had no doubts that that rhyme was about skin color preferances.

It's highly possible that the "If you're White" rhyme was probably part of folk culture for quite some time. But in 1951 Big Bill Broonzy recorded two versions of songs that included this rhyme.

Here's the lyrics to one of Big Bill Broonzy's songs:

BLACK, BROWN, AND WHITE(Version 1)
by Big Bill Broonzy
recording of September 20 1951, Paris

This little song that I'm singin' about,
people you know it's true
If you're black and gotta work for a living,
this is what they will say to you,
they says, "If you was white, should be all right,
if you was brown, stick around,
but as you's black, hmm brother, get back, get back, get back"

I was in a place one night
They was all having fun
They was all buyin' beer and wine,
but they would not sell me none
They said, "If you was white, should be all right,
if you was brown, stick around,
but if you black, hmm brother, get back, get back, get back"

Me and a man was workin' side by side
This is what it meant
They was paying him a dollar an hour,
and they was paying me fifty cent
They said, "If you was white, 't should be all right,
if you was brown, could stick around,
but as you black, hmm boy, get back, get back, get back"

I went to an employment office,
got a number 'n' I got in line
They called everybody's number,
but they never did call mine
They said, "If you was white, should be all right,
if you was brown, could stick around,
but as you black, hmm brother, get back, get back, get back"

I hope when sweet victory,
with my plough and hoe
Now I want you to tell me brother,
what you gonna do about the old Jim Crow?
Now if you was white, should be all right,
if you was brown, could stick around,
but if you black, whoa brother, get back, get back, get back

-snip-

see http://blueslyrics.tripod.com/artistswithsongs/big_bill_broonzy_1.htm#black_brown_and_white_version%201 for lyrics to more Bill Bill Broonzy songs including version #2 of this song.