Di Default la classe DateTimePicker non ha il metodo BackColor. Qualora dovessere diventare indispensabile nei vostri progetti ecco la classe che lo implementa:

Imports System

Imports System.ComponentModel

Imports System.Drawing

Imports System.Windows.Forms

Public Class ExtendedDateTimePicker

    Inherits DateTimePicker

    Private m_BackBrush As SolidBrush

    < _

        Browsable(True), _

        DesignerSerializationVisibility( _

            DesignerSerializationVisibility.Visible _

        ) _

    > _

    Public Overrides Property BackColor() As Color

        Get

            Return MyBase.BackColor

        End Get

        Set(ByVal Value As Color)

            If Not m_BackBrush Is Nothing Then

                m_BackBrush.Dispose()

            End If

            MyBase.BackColor = Value

            m_BackBrush = New SolidBrush(Me.BackColor)

            Me.Invalidate()

        End Set

    End Property

    Protected Overrides Sub WndProc(ByRef m As Message)

        Const WM_ERASEBKGND As Int32 = &H14

        If m.Msg = WM_ERASEBKGND Then

            Dim g As Graphics = Graphics.FromHdc(m.WParam)

            If m_BackBrush Is Nothing Then

                m_BackBrush = New SolidBrush(Me.BackColor)

            End If

            g.FillRectangle(m_BackBrush, Me.ClientRectangle)

            g.Dispose()

        Else

            MyBase.WndProc(m)

        End If

    End Sub

    Protected Overloads Overrides Sub Dispose( _

        ByVal disposing As Boolean _

    )

        If disposing AndAlso Not m_BackBrush Is Nothing Then

            m_BackBrush.Dispose()

        End If

        MyBase.Dispose(disposing)

    End Sub

End Class

Un solo piccolissimo problema: non funziona con lo style di Windows Vista.