As a matter of technique, you should print the value of $line before you change it to make sure it is what you think it is. In your second test, you need to escape the \ after Wayne. The following code should get you started:

$line = sprintf qq{Test #1 'Show me Waynes world','Jennys Basketball s
+hoes'\n};
print $line;   # <- added this line
$line =~ s/(')[^'\\]*(?:\\.[^'\\]*)*(')/$1SSS$2/g;
print $line;

$line = sprintf qq{Test #2 'Show me Wayne\\'s world','Jenny\\'s Basket
+ball shoes'\n};  # <- changed this line (two extra \ added)
print $line;   # <- added this line
$line =~ s/(')[^'\\]*(?:\\.[^'\\]*)*(')/$1SSS$2/g;
print $line;
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How to match quoted strings is discussed in many places, notably in Friedl's Mastering Regular Expressions O'Reilly book (the regex I used is derived from one in Friedl's book).

Update: Matching quoted strings is also discussed in perlre (in the "Quantifiers" section), where they suggest /"(?:[^"\\]++|\\.)*+"/ (perl 5.10 and above); see the discussion in perlre for more details. See also this stack overflow question and $RE{quoted} in Regexp::Common.