To construct a calendar appointment, the following C# code can be used:

// plaintext and HTML descriptions (HTML version is required by Outlook)
string bodyText = "Please come to project XYZ review meeting.";
string bodyHtml = "<p>Please come to project XYZ review meeting.</p>";

// appointment data - see http://tools.ietf.org/html/rfc2445 for details
string appointmentData =
    "BEGIN:VCALENDAR\n" +
    "PRODID:Rebex Mail\n" +
    "VERSION:2.0\n" +
    "BEGIN:VTIMEZONE\n" +
    "TZID:US-Eastern\n" +
    "BEGIN:STANDARD\n" +
    "DTSTART:19981025T020000\n" +
    "RDATE:19981025T020000\n" +
    "TZOFFSETFROM:-0400\n" +
    "TZOFFSETTO:-0500\n" +
    "TZNAME:EST\n" +
    "END:STANDARD\n" +
    "BEGIN:DAYLIGHT\n" +
    "DTSTART:19990404T020000\n" +
    "RDATE:19990404T020000\n" +
    "TZOFFSETFROM:-0500\n" +
    "TZOFFSETTO:-0400\n" +
    "TZNAME:EDT\n" +
    "END:DAYLIGHT\n" +
    "END:VTIMEZONE\n" +
    "BEGIN:VEVENT\n" +
    "DTSTAMP:19980309T231000Z\n" +
    "UID:guid-1.host1.com\n" +
    "ORGANIZER;ROLE=CHAIR:MAILTO:mrbig@host.com\n" +
    "ATTENDEE;RSVP=TRUE;ROLE=REQ-PARTICIPANT;CUTYPE=GROUP:MAILTO:employee-A@host.com\n" +
    "DESCRIPTION:Project XYZ Review Meeting\n" +
    "CATEGORIES:MEETING\n" +
    "CLASS:PUBLIC\n" +
    "CREATED:19980309T130000Z\n" +
    "SUMMARY:XYZ Project Review\n" +
    "DTSTART;TZID=US-Eastern:19980312T083000\n" +
    "DTEND;TZID=US-Eastern:19980312T093000\n" +
    "LOCATION:1CP Conference Room 4350\n" +
    "END:VEVENT\n" +
    "END:VCALENDAR\n";  

// construct the calendar view
AlternateView appointment = new AlternateView();
appointment.SetContent(appointmentData, "text/calendar");
appointment.ContentType.Parameters.Add("method", "REQUEST");

// construct the message
MailMessage message = new MailMessage();
message.BodyText = bodyText;
message.BodyHtml = bodyHtml;
message.AlternateViews.Add(appointment);

// save the message
message.Save(...);

To load and a calendar appointment and display its data, this should work:

// load the appointment
MailMessage appointment = new MailMessage();
appointment.Load(...);

// display text parts
Console.WriteLine("Plain text: {0}", appointment.BodyText);
Console.WriteLine("HTML text: {0}", appointment.BodyHtml);

// find and display the text/calendar part
foreach (AlternateView view in message.AlternateViews)
{
    if (view.ContentType.MediaType == "text/calendar")
    {
        Console.WriteLine("Appointment data: {0}", view.ContentString);
        break;
    }
}

If it still doesn't work for you, please let us know.

In case you prefer a message with a single text/calendar entity, you can use the following code to construct it:

string appointmentData =
    "BEGIN:VCALENDAR\n" +
    ... same as before ...
    "END:VCALENDAR\n";

// construct the calendar entity
MimeMessage appointment = new MimeMessage();
appointment.SetContent(appointmentData, "text/calendar");

// save the entity
appointment.Save(...);

The MimeMessage class is available in Rebex.Mime namespace. However, it looks like the other variant (text/calendar embedded in multipart/alternative) is slightly more compatible with third-party software (such as MS Outlook).

Again, instead of saving the MimeMessage, you can send it using the Smtp object.

The problem was the METHOD was not specified within the appointemt data and entity's Content-Type. This code works with my Outlook 2010. Please give it a try.

static string ConstructVCalendar(string from, string to, DateTime start, DateTime end, string summary, string description, string location)
{
    StringBuilder sb = new StringBuilder();
    sb.Append("BEGIN:VCALENDAR\n");
    sb.Append("METHOD:REQUEST\n");
    sb.Append("VERSION:2.0\n");
    sb.Append("PRODID:Rebex Mail\n");
    sb.Append("BEGIN:VEVENT\n");
    sb.AppendFormat("DTSTAMP:{0}\n", DateTime.Now.ToUniversalTime().ToString(@"yyyyMMdd\THHmmss\Z"));
    sb.AppendFormat("UID:{0}\n", Guid.NewGuid());
    sb.AppendFormat("ORGANIZER:MAILTO:{0}\n", from);
    sb.AppendFormat("ATTENDEE;RSVP=TRUE:MAILTO:{0}\n", to);
    sb.AppendFormat("DTSTART:{0}\n", start.ToUniversalTime().ToString(@"yyyyMMdd\THHmmss\Z"));
    sb.AppendFormat("DTEND:{0}\n", end.ToUniversalTime().ToString(@"yyyyMMdd\THHmmss\Z"));
    sb.Append("CATEGORIES:MEETING,PROJECT\n");
    sb.Append("CLASS:PUBLIC\n");
    sb.AppendFormat("SUMMARY:{0}\n", summary);
    sb.AppendFormat("DESCRIPTION:{0}\n", description);
    sb.AppendFormat("LOCATION:{0}\n", location);
    sb.Append("END:VEVENT\n");
    sb.Append("END:VCALENDAR\n");
    return sb.ToString();
}

// ...
string from = "organizer@host.com";
string to = "attendee@host.cz";
DateTime start = new DateTime(2011, 2, 28, 10, 30, 0, DateTimeKind.Local);
DateTime end = start.AddHours(2); // duration is 2 hours

// appointment data - see http://tools.ietf.org/html/rfc2445 for details
string appointmentData = ConstructVCalendar(from, to, start, end, "My summary", "My description", "My location");

// construct the calendar entity
MimeMessage appointment = new MimeMessage();
appointment.SetContent(appointmentData, "text/calendar");
appointment.ContentType.Parameters.Add("method", "REQUEST");
appointment.From = from;
appointment.To = to;

Smtp.Send(appointment, "SMTP.server.name");

Please note the line sb.AppendFormat("UID:{0}\n", Guid.NewGuid()); This UID can be used lately to change this appointemnt.