The artist and name of the song that begins "I looked out of my
window, and what do you think I saw, I saw two buffaloes, two
buffaloes, two buffaloes on my lawn.."

Hello and thank you for your question.

The song you’re referring to is “Two Buffalos” performed by Rolf
Harris.

I can only post a small part of the lyrics here because of copyright
reasons.

“I looked outside my window
And what do you think I saw
The strangest sight I've ever seen
You'll never guess just what I mean
I can't believe it myself

I saw two buffalos
Two buffalos
Buffalos on my lawn
Rompin' all around and stompin' on the ground
And all of my grass was gone.”

The song “Two Buffalos” was released on Epic 45 #9682.  The flip is
called "The Court of King Caractacus”.

The complete lyrics to the song “Two Buffalos” may be found at the
following Google Newsgroup posting:
http://groups.google.com/groups?q=%22two+buffalos%22+lyrics&hl=en&lr=&ie=UTF-8&oe=UTF-8&selm=3524529d.8153012%40news.abs.net&rnum=1


The Classic 45īs website carries the single Two Buffalos.

Harris, Rolf  
The Court of King Caractacus/ Two Buffalos 
Epic 9682, 1964
Price: $10.00    
http://www.classic45s.com/advanced_search_result.php?PHPSESSID=&keywords=buffalos&type=name&x=11&y=7

Amazon carries a number of CDs by Rolf Harris although “Two Buffalos”
is not included in any of them.
http://www.amazon.com/exec/obidos/search-handle-form/002-7789571-7981607


Additional information that may interest you:

The Music of Rolf Harris
http://www.rolfharrissongs.pwp.blueyonder.co.uk/links.htm

Rolf Harris Website
http://www.rolfharris.com/


Search Criteria:

"two buffalos" lyrics
"Rolf Harris" "two buffalos"

I hope you find this helpful.

Best Regards,
Bobbie7-ga

I am highly pleased with  the speed of he answer, as I was in the 
process of writing an article where I could use the answer, and also
pleased with not only the apparent accuracy(I assume it's accurate)
but with the extra information the researcher provided.