If you want to use $.getJSON() you can add the following before the call :
$.ajaxSetup({ scriptCharset: "utf-8" , contentType: "application/json; charset=utf-8"});
You can use the charset you want instead of utf-8.
The options are explained here.
contentType : When sending data to the server, use this content-type. Default is "application/x-www-form-urlencoded", which is fine for most cases.
scriptCharset : Only for requests with 'jsonp' or 'script' dataType and GET type. Forces the request to be interpreted as a certain charset. Only needed for charset differences between the remote and local content.
You may need one or both ...