There is a town in New Mexico, about fifty miles from Santa Fe, which bears the name of Abiquiu. It's pronounced "Abacue". That fits better with the song.
I can't find the song listed as one of the songs Smiley wrote, and I can't find any info about it.
So here's the song, yet again, with the new an improved location.
Giddy Up, Jericho, I lay the whip, away we go to Abiquiu Abiquiu Abiquiu Abiquiu (pronounced "Abacue") Giddyup, Jericho, she's waiting there for me you know (still pensive on that one) 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 Abiquiu Abiquiu Abiquiu Abiquiu 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 Abiquiu Abiquiu Abiquiu Abiquiu Giddayup,Jericho, she's waiting there for me you know my Suzi-que, my Suzi-que, my Suzi-que, my Suzi-que Suuuuuziiiiiquuuuuue!