NewtonSoft.Json 具有难以理解的结构，您可以使用以下自定义转换器之类的工具来执行所需的操作：

[TestMethod]
public void Conversion()
{
    var obj = new DualDate()
    {
        DateOne = new DateTime(2013, 07, 25),
        DateTwo = new DateTime(2013, 07, 25)
    };
    Assert.AreEqual("{\"DateOne\":\"07.25.2013\",\"DateTwo\":\"2013-07-25T00:00:00\"}", 
        JsonConvert.SerializeObject(obj, Formatting.None, new DualDateJsonConverter()));
}

class DualDate
{
    public DateTime DateOne { get; set; }
    public DateTime DateTwo { get; set; }
}

class DualDateJsonConverter : JsonConverter
{

    public override void WriteJson(JsonWriter writer, object value, JsonSerializer serializer)
    {

        JObject result = new JObject();

        DualDate dd = (DualDate)value;

        result.Add("DateOne", JToken.FromObject(dd.DateOne.ToString("MM.dd.yyyy")));
        result.Add("DateTwo", JToken.FromObject(dd.DateTwo));
        result.WriteTo(writer);
    }

    // Other JsonConverterMethods
    public override bool CanConvert(Type objectType)
    {
        return objectType == typeof(DualDate);
    }

    public override bool CanWrite
    {
        get
        {
            return true;
        }
    }
    public override bool CanRead
    {
        get
        {
            return false;
        }
    }

    public override object ReadJson(JsonReader reader, Type objectType, object existingValue, JsonSerializer serializer)
    {
        throw new NotImplementedException();
    }
}