PrivatePropertyJson.cs

namespace MCVE {
    using System;
    using System.Reflection;

    using JsonNet.PrivateSettersContractResolvers;

    using Newtonsoft.Json;
    using Newtonsoft.Json.Serialization;

    internal struct RootObject {
        private string name { get; set; }

        public string ExampleGetter => name;
    }

    internal class Program {
        private static void Main(string[] args) {
            var jsonString = @"{ 'name': 'Generic Rocket' }";

            var privateResolverSettings = new JsonSerializerSettings { ContractResolver = new PrivateResolver() };
            var outsideResolver = new JsonSerializerSettings { ContractResolver = new PrivateSetterContractResolver() };

            //var deserialized = JsonConvert.DeserializeObject<RootObject>(jsonString);
            //var deserialized = JsonConvert.DeserializeObject<RootObject>(jsonString, outsideResolver);
            var deserialized = JsonConvert.DeserializeObject<RootObject>(jsonString, privateResolverSettings);

            Console.WriteLine(deserialized.ExampleGetter);
        }
    }

    internal class PrivateResolver : DefaultContractResolver {
        protected override JsonProperty CreateProperty(MemberInfo member, MemberSerialization memberSerialization) {
            var prop = base.CreateProperty(member, memberSerialization);
            if (!prop.Writable) {
                var property = member as PropertyInfo;

                if (property != null) {
                    var hasPrivateSetter = property.GetSetMethod(true) != null;
                    prop.Writable = hasPrivateSetter;
                }
            }

            return prop;
        }
    }
}