Modify existing object with new partial JSON data using Json.NET

You want JsonSerializer.Populate() or its static wrapper method JsonConvert.PopulateObject():

Populates the JSON values onto the target object.

For instance, here it is updating an instance of your Calendar class:

public static class TestPopulate
{
    public static void Test()
    {
        var calendar = new Calendar
        {
            Id = 42,
            CoffeeProvider = "Espresso2000",
            Meetings = new[]
            {
                new Meeting
                {
                    Location = "Room1",
                    From = DateTimeOffset.Parse("2014-01-01T00:00:00Z"),
                    To = DateTimeOffset.Parse("2014-01-01T01:00:00Z")
                },
                new Meeting
                {
                    Location = "Room2",
                    From = DateTimeOffset.Parse("2014-01-01T02:00:00Z"),
                    To = DateTimeOffset.Parse("2014-01-01T03:00:00Z")
                },
            }
        };

        var patch = @"{
    'coffeeprovider': null,
    'meetings': [
        {
            'location': 'Room3',
            'from': '2014-01-01T04:00:00Z',
            'to': '2014-01-01T05:00:00Z'
        }
    ]
}";
        Patch(calendar, patch);

        Debug.WriteLine(JsonConvert.SerializeObject(calendar, Formatting.Indented));
    }

    public static void Patch<T>(T obj, string patch)
    {
        var serializer = new JsonSerializer();
        using (var reader = new StringReader(patch))
        {
            serializer.Populate(reader, obj);
        }
    }
}

And the debug output produced is:

{
  "id": 42,
  "coffeeprovider": null,
  "meetings": [
    {
      "location": "Room3",
      "from": "2014-01-01T04:00:00+00:00",
      "to": "2014-01-01T05:00:00+00:00"
    }
  ]
}

Update

If you want to copy first, you could do:

    public static T CopyPatch<T>(T obj, string patch)
    {
        var serializer = new JsonSerializer();

        var json = JsonConvert.SerializeObject(obj);
        var copy = JsonConvert.DeserializeObject<T>(json);

        using (var reader = new StringReader(patch))
        {
            serializer.Populate(reader, copy);
        }

        return copy;
    }