Eupher, my code sends a 'Task'. It can't be that different to send an appointment. As a trial I changed the dim to 'Appointment3' and ("GW.MESSAGE.TASK"

to ("GW.MESSAGE.APPOINTMENT"

and commented out some lines that were clearly pertaining to sending a task. It worked, except that you would need to add some lines on appt times etc.
If you can't get SendObject to work, try this.
GW Library Items are required
'/*****************************************************
Public Function StartExport()
Application.Echo True, "Creating Email"
DoCmd.SelectObject acForm, "Mail Letters"
Dim objGWApp As Object
Dim objGWAcct As Object
Dim objGWmsg As Object
Dim objGWTask As Task3
Dim strContactEmail, strBody, strSubject, strExm As String
' set contact email address to variable
strContactEmail = Me.hylkEmail.Value
'set body of email to variable
strBody = "To: " & Me.txtCoContact & Chr(10) _
& " " & Me.txtCoName & Chr(10) _
& " " & Me.txtAdd1 & Chr(10) _
& " " & Me.txtCityStZip & Chr(10) & Chr(10) _
& "your text here.
strSubject = ""
On Error GoTo ErrHandler
' create new email
Set objGWApp = CreateObject("NovellGroupWareSession"

Set objGWAcct = objGWApp.Login("FAFilings", "password"

Set objGWmsg = objGWAcct.MailBox.Messages
Set objGWmsg = objGWmsg.Add()
'if cboltrtype is FAX, then skip the send
objGWmsg.FromText = ""
objGWmsg.Recipients.Add strContactEmail
End If
objGWmsg.BodyText = strBody
objGWmsg.Subject = strSubject
objGWmsg.Recipients.Add "", , 2
objGWmsg.Attachments.Add strCoverLtr
objGWmsg.Send
'add a new task object to the calendar
Set objGWTask = objGWAcct.Calendar.Messages.Add("GW.MESSAGE.TASK"

objGWTask.OnCalendar = True
'set the properties of the message object
objGWTask.FromText = ""
objGWTask.Recipients.Add ""
objGWTask.Recipients.Resolve
objGWTask.StartDate = Format(Now(), "short date"

objGWTask.DueDate = Format(Now() + 20, "short date"

objGWTask.Subject = Me.txtCoName
objGWTask.BodyText = strSubject & " ; " & Format(Now(), "short date"

objGWTask.NotifyWhenAccepted = egwNotify
objGWTask.NotifyWhenDeclined = egwNotify
'Send the task message
objGWTask.Send
On Error Resume Next
Set objGWApp = Nothing
Set objGWmsg = Nothing
Set objGWAcct = Nothing
Set objGWTask = Nothing
Exit Function
ExitHere:
Exit Function
ErrHandler:
Err.Raise Err.Number, Err.Source, Err.DESCRIPTION
Resume ExitHere
End Function