Try this:
HttpCookie objCookie = new HttpCookie(cookiename);
objCookie.Values.Add(cookiename, cookievalue);
DateTime dtExpiry = DateTime.Now.AddDays(iDaysToExpire);
Response.Cookies.Clear();
Response.Cookies.Add(objCookie);
Response.Cookies[cookiename].Expires = dtExpiry;
I have just changed the order of attaching the cookie to the response. Once you have make the Cookie, add values to it then add it to the response.