日付ピッカーの代わりに、Excel のすべての日付列で自動入力を使用しています。下記を参照してください。
Private Sub Worksheet_SelectionChange(ByVal Target As Range)
Dim xRg As Range, xCell As Range
On Error Resume Next
If (Target.Count = 1) Then
If (Not Application.Intersect(Target, Me.Range("H4,H7")) Is Nothing) Then _
Target.Offset(0, x1down) = Date
Application.EnableEvents = False
Set xRg = Application.Intersect(Target.Dependents, Me.Range("H4,H7"))
If (Not xRg Is Nothing) Then
For Each xCell In xRg
xCell.Offset(0, x1down) = Date
Next
End If
Application.EnableEvents = True
End If
End Sub