There are several ports he could have entered by, but the most common were Sydney (New South Wales) or Melbourne(Victoria). I checked the NSW records and found these two marriages, which could relate to your relative:
705/1893 LINDNER CHARLES O'ROURKE CATHERINE SYDNEY
3066/1893 LINDNER ERNST A SANGER ALICE COROWA
There was no Ernst/Ernest in the death records but there were three Carl/Charles
LINDNER CARL AUGUST 18158/1936 AUGUST HEINERETTA
District HENTY
LINDNER CHARLES A 7786/1935 JOHANN A LOUISA
District CULCAIRN
LINDNER CARL W H 11959/1899 GODLIPP AMELIA
District ALBURY
None of these appear to be him, based on the info you gave, but I included them.
I will look in Victorian records in a moment,