How would you convert a String to a Java string literal?

If you can add external code, Apache's Commons Text has StringEscapeUtils.escapeJava() which I think does exactly what you want.

My naive state machine implementation looks like this:

public String javaStringLiteral(String str)
{
    StringBuilder sb = new StringBuilder("\"");
    for (int i=0; i<str.length(); i++)
    {
        char c = str.charAt(i);
        if (c == '\n')
        {
            sb.append("\\n");
        }
        else if (c == '\r')
        {
            sb.append("\\r");
        }
        else if (c == '"')
        {
            sb.append("\\\"");
        }
        else if (c == '\\')
        {
            sb.append("\\\\");
        }
        else if (c < 0x20)
        {
            sb.append(String.format("\\%03o", (int)c));
        }
        else if (c >= 0x80)
        {
            sb.append(String.format("\\u%04x", (int)c));
        }
        else
        {               
            sb.append(c);
        }
    }
    sb.append("\"");
    return sb.toString();
}