Thanks, SRS! It helps! This is what I hear (I've got the same accent as he does, roughly):

Giddy Up, Jericho, I lay the whip, away we go to
Albuquerque, Albuquerque, Albuquerque, Albuquerque (pronounced "Albu-que" each time)
Giddayup, a Jericho, she's waiting there for me and n/or my Suzi-que, my Suzi-que, my Suzi-que, my Suzi-que,
Roses in her hair
She'll say pale face glad you're here
Oh, that cutie pie
Me get sleepy in a teepee? Not me! (whooping)
Oh
Giddy Up, Jericho, I lay the whip, away we go to
Albuquerque, Albuquerque, Albuquerque, Albuquerque
Giddayup,Jericho, she's waiting there for me you know[?] my Suzi-que, my Suzi-que, my Suzi-que, my Suzi-que Suuuuuziiiii quuuuue!
(piano)
With Roses in her hair,
She'll say "Paleface, glad you're here!"
Oh, that cutie pie!
Me get sleepy in a teepee? Not me! (whooping)
Oh Giddy Up, Jericho, I lay the whip, away we go to
Albuquerque, Albuquerque, Albuquerque, Albuquerque
Giddayup,Jericho, she's waiting there for me you know[?] my Suzi-que, my Suzi-que, my Suzi-que, my Suzi-que Suuuuuziiiii quuuuuue!

So pretty much it's the same thing over three times. SRS, you helped me piece together a few of the words I couldn't catch. Thanks!