"The Riff Song", by Romberg, is available on reproducing rolls:

Ampico:
   67713 Desert Song Selections, played by Fairchild and Rainger
  208431 The Riff Song, played by Carroll
Duo-Art:
  713332 The Riff Song played by Moran & Feldcamp
  British 0787   ditto
Welte:
   75171 Desert Song Selections played by Rodney

David Sharpe