オブジェクトをJSON文字列（UNICODE）に変換する

var obj = {"key":"ü"};
var str1 = JSON.stringify(obj);
var str2 = "";
var chr = "";
for(var i = 0; i < str1.length; i++){
    if (str1[i].match(/[^\x00-\x7F]/)){
        chr = "\\u" + ("000" + str1[i].charCodeAt(0).toString(16)).substr(-4);
    }else{
        chr = str1[i];
    }
    str2 = str2 + chr;
}  
console.log(str2); 

>>{"key":"\u00fc"}

javascript - JSON.stringify and unicode characters - Stack Overflow