Works with no annotations...

gistfile1.txt

        [Fact]
        public void Should_serialize_Test()
        {
            var sets = new DataContractJsonSerializerSettings { SerializeReadOnlyTypes = true };

            Test test = new Test { Name = "name", City = "city" };
            DataContractJsonSerializer js = new DataContractJsonSerializer(typeof(Test), sets);
            MemoryStream ms = new MemoryStream();
            js.WriteObject(ms, test);
            ms.Position = 0;
            StreamReader sr = new StreamReader(ms);
            string serialized = sr.ReadToEnd();
            sr.Dispose();
            ms.Dispose();
            
            serialized.ShouldBeEquivalentTo("{\"City\":\"city\",\"Name\":\"name\"}");
        }
    
    public class Test : ISerializable
    {
        public bool IsFailure { get; }
        public string Name;
        public string City;

        void ISerializable.GetObjectData(SerializationInfo oInfo, StreamingContext oContext)
        {
            oInfo.AddValue("IsFailure", IsFailure);
            oInfo.AddValue("Name", Name);
            if (IsFailure)
            {
                oInfo.AddValue("City", City);
            }
        }
    }