To use a custom date, you can use the style.Format property to set the format.
GridStyleInfo style = this.gridControl1[1,2];
style.CellType = "MonthCalendar";
style.CellValueType = typeof(DateTime);
style.Format = "dd/MM/yy HH.mm.ss";
style.CellValue = DateTime.Now;
But if you specify the format that is not consistent with the regional settings for dates, this will cause the grid to throw an exception as you try to drop the calendar. This is not a problem if you are not allowing editing, or if the format is consistent with the regional setting. But if you do run into the problem, one way to work around it is to derive the cell control and set the value into the calendar dropdown taking into account the format provided in the style.
Here is a sample. This sample has both the custom celltype that handles the format, as well as several grid events that can also do the same thing. To see the grid events work, add this code to set one of the cells to use the standard MonthCalendar.
//uses events to set a format
style = this.gridControl1[5,2];
style.CellType = "MonthCalendar";
style.CellValueType = typeof(DateTime);
style.Format = "MM/dd/yy HH.mm.ss";
style.BackColor = Color.LightGoldenrodYellow;
style.CellValue = DateTime.Now;