I\'m trying to replace the \"\'\" character with the \"\'\'\" string using the replace method, like this:
temp.replace(\"\\\'\", \"\'\'\");
but
You're actually trying to replace (\'), not just the single quote character. There is no need to escape a single quote in a string delimited by double quotes, because they don't signify the end of a string...
Replace will only replace the first quote matched, unless you're using our old friend Regexp. The downside being Regular Expressions tend to be slow. I haven't checked to see which is faster, but you could try using split:
var chunks = temp.split("'").join("''");
test = "string cont'aining single 'quotes".split("'").join("''");//in firebug console
//returns "string cont''aining single ''quotes" as expected