So far the only film I have been able to find pictures for is
This was an Allied Artists' film that came out in February, 1962. The writers and directors were Dorrell McGowan and Stuart E. McGowan. The star of the film is an 8 year old Hungarian girl (Tristie) who escapes from an orphan camp in Hungary and manages to get into Austria with the aid of a Hungarian border guard dog - the Irish wolfhound - which turns against the border guards in order to accompany her.
The police in Austria promise to help her find the new loving family she is seeking, but she discovers that means being put into an orphanage and being separated from the dog, so she escapes again and joins a circus owned by Kurt (played by Helmut Schmid), where she becomes friendly with the elephant of the title.
Kurt is in the middle of an unpleasant divorce but his girlfriend, Steffi, decides she needs to marry him so that she can adopt Tristie, but more complications arise with the Salzburg police attempting to take Tristie into custody and, when they are defied by the elephant and the dog, threaten to shoot both of them, so Tristie slips away to give herself up but is followed by her four-footed friends, and decides the only course is for them to run away together.
Lost in the narrow streets she finds refuge in St. Peter's Church but is knocked unconscious by a fall down steep steps, picked up by the elephant and taken back to the circus, where eventually there is a climax that brings about a happy conclusion to the story.
The elephant, Valle, was obtained from a Danish circus; the Irish wolfhound, Jeffrey, from Hollywood. The production was filmed in Germany with an American production crew. Molly McGowan (as Molly Mack)(12 years old) played Tristie.
So who was Jeffrey? He was Fleetwind Jeffrey, owned by John Scheiner, who trained animals for films and found Irish wolfhounds were particularly good actors and actresses. At the time of this film - which was first entitled "No Time to Cry" - the Scheiners had five wolfhounds.
Unfortunately, the film did not do very well - at some time, apparently, its name was changed from The Bashful Elephant to TRISTIE (going by the posters shown here) but that didn't seem to help - so there is no video or DVD of it for present-day wolfhound lovers to enjoy. However, it may be possible to have this film produced on DVD, so add your vote on http://www.tcm.com/tcmdb/title.jsp?stid=68160