Had a quick look in - Index to photographs of WWI servicemen and women in the Tasmanian weekly magazines. Volume 1, The Weekly Courier / compiled by Wendy K.Knolle but couldn't see a Francis Joseph CUNNINGHAM??
Most of the entries have surname and initials, not full names. The closest I could see was CUNNINGHAM, Private F. E. of Launceston 15 March 1917 pg. 24
There are other general indexes to the Weekly Courier and if I get a chance will check them but I would have thought this was the most obvious one to find him. Was the portrait just of Francis Joseph or was it a group shot??
Cheers,
Peter