Based on the information you provided, the most likely Australian band with 4 letters in its name whose songs might evoke feelings of sadness or include lyrics about tears is:
- The Saints ( )
The Saints are an influential Australian rock band formed in Brisbane in 1973. Their music is known for its raw energy and often deals with dark themes. While they don’t have a song explicitly titled “Bitter Tears”, some of their songs, like “(I’m) Stranded” and “Know Your Product”, have a melancholic vibe that could be interpreted as conveying feelings of sadness or heartbreak.