Your question seems to be more about PHP than Javascript, based on the code snippet you provided. Basically, you might want to escape the apostrophes with a backslash character.
onclick="(method('<?php echo $variable; ?>'))"
would then become something like this perhaps:
onclick="(method('<?php echo addslashes($variable); ?>'))"
… and please remove the parenthesis you have surrounding the onclick event, like so:
onclick="method('<?php echo addslashes($variable); ?>')"
solved JavaScript String Handling