The one that goes “I am the King of Siam; yes I am” to the tune of the Mexican Hat Dance song. All Google could tell me is that someone else somewhere in the world had heard this too because it was quoted with no context on a website on an unrelated topic. Does anyone have a source for this?
The only “Siam” song I know which is even close to that is by Spike Jones.
There’s “Old Siam, Sir” by McCartney and Wings on the Back to the Egg album, but I don’t imagine that’s the one you’re looking for.
I’m quite sure it’s not the song you’re looking for, but here’s another one with that theme, Frank Black and the Catholics’ “King And Queen Of Siam”.
My thought was the poem “Dynastic Tiff”, by Geoffrey Hellman:
“Oh I am the King of Siam, I am!
With cunning I rule from Bangkok.
The King of Bagdad is a sham, a sham,
While I am the King of Siam. (I am.)…” etc.
The whole thing can be found here (search for “Siam”).
That’s as close as anything I’ve found so far.