var jsonData = {a:1,b:2};

function obj2string(o) {
    var r = [];
    if (typeof o == "string") {
        return "\"" + o.replace(/([\'\"\\])/g, "\\$1").replace(/(\n)/g, "\\n").replace(/(\r)/g, "\\r").replace(/(\t)/g, "\\t") + "\"";
    }
    if (typeof o == "object") {
        if (!o.sort) {
            for (var i in o) {
                r.push(i + ":" + obj2string(o[i]));
            }
            if ( !! document.all && !/^\n?function\s*toString\(\)\s*\{\n?\s*\[native code\]\n?\s*\}\n?\s*$/.test(o.toString)) {
                r.push("toString:" + o.toString.toString());
            }
            r = "{" + r.join() + "}";
        } else {
            for (var i = 0; i < o.length; i++) {
                r.push(obj2string(o[i]))
            }
            r = "[" + r.join() + "]";
        }
        return r;
    }
    return o.toString();
}

jsonData = obj2string(jsonData);
console.log(jsonData);