Aha! I found it here

My Pony Boy
Words: Bobby Heath
Music: Charley O'Donnell
Producer: F. Ziegfeld, Jr.
Published in 1909

  Way out west, in a nest from the rest dwelt 
      the bestest little Broncho Boy;
  He could ride, he could glide o'er the 
      prairies like an arrow.
  Ev'ry maid in the glade, was afraid he would 
      trade his little heart away,
  So each little peach made a nice little speech 
      of love to him.
  
  Till one day, out that way, so they say, came to stay a 
      Fluffy Ruffle girl.
  She made eyes, she surprised, and he found his 
      heart was lassoed.
  When he thought he was caught, how he fought, 
      but she taught this pony boy to love.
  But he balked when she talked of a trip to New York, 
      so she sang to him:
  
  Chorus:
  Pony Boy, Pony Boy, won't you be my Tony Boy?
  Don't say no.  Here we go off across the plains;
  Marry me, carry me right away with you-
  Giddy up, giddy up, giddy up, Whoa! My Pony Boy.