C#

using System;
using System.Windows.Forms;

namespace DGV_DateTimePicker
{
    public class DateTimePickerColumn : DataGridViewColumn
    {
        public DateTimePickerColumn()
            : base(new DateTimePickerCell())
        {
        }

        public override DataGridViewCell CellTemplate
        {
            get
            {
                return base.CellTemplate;
            }
            set
            {
                // Ensure that the cell used for the template is a DateTimePickerCell.
                if (value != null &&
                    !value.GetType().IsAssignableFrom(typeof(DateTimePickerCell)))
                {
                    throw new InvalidCastException("Must be a DateTimePickerCell");
                }
                base.CellTemplate = value;
            }
        }
    }

    public class DateTimePickerCell : DataGridViewTextBoxCell
    {

        public DateTimePickerCell()
            : base()
        {
            // Use the custom defined date format.
            this.Style.Format = "dd MMM yyyy";
        }

        public override void InitializeEditingControl(int rowIndex, object
            initialFormattedValue, DataGridViewCellStyle dataGridViewCellStyle)
        {
            // Set the value of the editing control to the current cell value.
            base.InitializeEditingControl(rowIndex, initialFormattedValue,
                dataGridViewCellStyle);

            DateTimePickerEditingControl ctl = (DateTimePickerEditingControl)DataGridView.EditingControl;
            DateTime d;
            ctl.Value = DateTime.TryParse((Value ?? "").ToString(), out d) ? d : DateTime.Now;

            /*Check whether the datagridview is databound/unbound. In both cases if the value of the cell
		 isn't null then check the DateTimePickerEditing Control else uncheck it.*/
            if (ctl.EditingControlDataGridView.CurrentCell.OwningColumn.IsDataBound)
                ctl.Checked = Value.ToString() == "" ? false : Value == null ? false : true;
            else
                ctl.Checked = Value == null ? false : true;
        }

        public override Type EditType
        {
            get
            {
                // Return the type of the editing contol that DateTimePickerCell uses.
                return typeof(DateTimePickerEditingControl);
            }
        }

        public override Type ValueType
        {
            get
            {
                // Return the type of the value that DateTimePickerCell contains.
                return typeof(DateTime);
            }
        }

        public override object DefaultNewRowValue
        {
            get
            {
                //Return null as the default value for new row.
                return null;
            }
        }
    }

    class DateTimePickerEditingControl : DateTimePicker, IDataGridViewEditingControl
    {
        DataGridView dataGridView;
        private bool valueChanged = false;
        int rowIndex;

        public DateTimePickerEditingControl()
        {
            this.Format = DateTimePickerFormat.Custom;
            this.CustomFormat = "dd MMM yyyy";
            this.ShowCheckBox = true;
            this.Checked = false;
        }

        // Implements the IDataGridViewEditingControl.EditingControlFormattedValue 
        // property.
        public object EditingControlFormattedValue
        {
            get
            {
                return this.Value.ToShortDateString();
            }
            set
            {
                if (value is String)
                {
                    this.Value = DateTime.Parse((String)value);
                }
            }
        }

        // Implements the 
        // IDataGridViewEditingControl.GetEditingControlFormattedValue method.
        public object GetEditingControlFormattedValue(
            DataGridViewDataErrorContexts context)
        {
            return EditingControlFormattedValue;
        }

        // Implements the 
        // IDataGridViewEditingControl.ApplyCellStyleToEditingControl method.
        public void ApplyCellStyleToEditingControl(
            DataGridViewCellStyle dataGridViewCellStyle)
        {
            this.Font = dataGridViewCellStyle.Font;
            this.CalendarForeColor = dataGridViewCellStyle.ForeColor;
            this.CalendarMonthBackground = dataGridViewCellStyle.BackColor;
        }

        // Implements the IDataGridViewEditingControl.EditingControlRowIndex 
        // property.
        public int EditingControlRowIndex
        {
            get
            {
                return rowIndex;
            }
            set
            {
                rowIndex = value;
            }
        }

        // Implements the IDataGridViewEditingControl.EditingControlWantsInputKey 
        // method.
        public bool EditingControlWantsInputKey(
            Keys key, bool dataGridViewWantsInputKey)
        {
            // Let the DateTimePicker handle the keys listed.
            switch (key & Keys.KeyCode)
            {
                case Keys.Left:
                case Keys.Up:
                case Keys.Down:
                case Keys.Right:
                case Keys.Home:
                case Keys.End:
                case Keys.PageDown:
                case Keys.PageUp:
                    return true;
                default:
                    return !dataGridViewWantsInputKey;
            }
        }

        // Implements the IDataGridViewEditingControl.PrepareEditingControlForEdit 
        // method.
        public void PrepareEditingControlForEdit(bool selectAll)
        {
            // No preparation needs to be done.
        }

        // Implements the IDataGridViewEditingControl
        // .RepositionEditingControlOnValueChange property.
        public bool RepositionEditingControlOnValueChange
        {
            get
            {
                return false;
            }
        }

        // Implements the IDataGridViewEditingControl
        // .EditingControlDataGridView property.
        public DataGridView EditingControlDataGridView
        {
            get
            {
                return dataGridView;
            }
            set
            {
                dataGridView = value;
            }
        }

        // Implements the IDataGridViewEditingControl
        // .EditingControlValueChanged property.
        public bool EditingControlValueChanged
        {
            get
            {
                return valueChanged;
            }
            set
            {
                valueChanged = value;
            }
        }

        // Implements the IDataGridViewEditingControl
        // .EditingPanelCursor property.
        public Cursor EditingPanelCursor
        {
            get
            {
                return base.Cursor;
            }
        }

        protected override void OnValueChanged(EventArgs eventargs)
        {
            // Notify the DataGridView that the contents of the cell
            // have changed.
            valueChanged = true;
            this.EditingControlDataGridView.NotifyCurrentCellDirty(true);
            base.OnValueChanged(eventargs);
        }
    }
}

private void Form1_Load(object sender, EventArgs e)
{
    DateTimePickerColumn col = new DateTimePickerColumn();
    dataGridView1.Columns.Add(col);
    dataGridView1.RowCount = 5;
}