.NET (Core and Framework)

using System;
using System.Windows.Forms;

public class DateTimeBinding : Binding
{
   public DateTimeBinding(string propertyName, object dataSource, string dataMember) 
      : base(propertyName, dataSource, dataMember)
   {}
 
   protected override void OnFormat(ConvertEventArgs e)
   {
      if (e.DesiredType == typeof(DateTime))
      {
         if (e.Value is DBNull)
            e.Value = DateTimePicker.MinDateTime;
      }
      else if (e.DesiredType == typeof(bool))
      {
         if (e.Value is DBNull)
            e.Value = false;
         else
            e.Value = true;
      }
 
      base.OnFormat(e);
   }
 
   protected override void OnParse(ConvertEventArgs e)
   {
      if (e.DesiredType == typeof(DateTime)
         && e.Value is DateTime
         && (DateTime)e.Value == DateTimePicker.MinDateTime)
 
         e.Value = DBNull.Value;
 
      else if (e.DesiredType == typeof(bool)
         && e.Value is bool
         && (bool)e.Value == false)
 
         e.Value = DBNull.Value;
 
      base.OnParse(e);
   }
}

dtp.ShowCheckBox = true;
dtp.DataBindings.Add(new DateTimeBinding("Value", ds, "[Date Field]"));
dtp.DataBindings.Add(new DateTimeBinding("Checked", ds, "[Date Field]"));