public class Student{
    public int Id{get;set;}
    public string Name{get;set;}
    public DateTime BirthDay{get;set;}
}

Student stu = new Student()
{
    Id = 1,
    Name = "zhangsan",
    BirthDay = DateTime.Now
};
String result = Newtonsoft.Json.JsonConvert.SerializeObject(stu);
Console.WriteLine(result);
Console.ReadLine();

Student stu = new Student()
{
    Id = 1,
    Name = "zhangsan",
    BirthDay = DateTime.Now
};
Newtonsoft.Json.Converters.IsoDateTimeConverter timeConverter = new Newtonsoft.Json.Converters.IsoDateTimeConverter();
//这里使用自定义日期格式，如果不使用的话，默认是ISO8601格式
timeConverter.DateTimeFormat = "yyyy-MM-dd HH:mm:ss";
String result = Newtonsoft.Json.JsonConvert.SerializeObject(stu, Newtonsoft.Json.Formatting.None, timeConverter);
Console.WriteLine(result);
Console.ReadLine();