Making a simple call to a server
You are correct. There is a better way. Starting in .NET 3.5, there is a JavaScriptSerializer class that can be used for simplifying JSON responses. It can be found in the System.Web.Script.Serialization namespace (System.Web.Extensions assembly)

First, you'd need to make a model to represent your response:

public class SimpleResponse {
    public string responseDateTime { get; set; }

    public SimpleResponse() {
          responseDateTime = "hello hello there!";
    }
}


...Then in your handler:

 public void ProcessRequest(HttpContext context)
 {
     context.Response.ContentType = "application/json";
     var json = new JavaScriptSerializer();

     context.Response.Write(
         json.Serialize(new SimpleResponse())
     );    
 }


Here is the result:

{"responseDateTime":"hello hello there!"}


In an ASP.NET MVC application this is more trivial. Just return a JsonResult from your controller:

public JsonResult Index()
{
    return Json(new SimpleResponse());
}