The song is properly called I'LL BE THERE, I'LL BE THERE, MARY DEAR and it was indeed written by Andrew B. Sterling (words) and Harry Von Tilzer (music), copyright 1902. The Library of Congress American Memory Collection doesn't have a complete copy (not online anyway) but it does have the first page which appeared as an advertisement on the back of the sheet music for a different song. The words on that first page correspond pretty closely to what Gene Autry sang, and what Guest John posted above.