Yes, it is possible.
Assuming your MDI Child is Form2:
Public Class Form2
Private thisMenu As ContextMenu
Private Sub Form2_Load(sender As Object, e As System.EventArgs) Handles Me.Load
thisMenu = New ContextMenu
Dim item1 As New MenuItem("entry1", AddressOf Item1_Click, Nothing)
Dim item2 As New MenuItem("entry2", AddressOf Item2_Click, Nothing)
thisMenu.MenuItems.Add(item1)
thisMenu.MenuItems.Add(item2)
End Sub
Private Sub Form2_MouseUp(sender As Object, e As System.Windows.Forms.MouseEventArgs) Handles Me.MouseUp
If e.Button = MouseButtons.Right Then
thisMenu.Show(Me, e.Location)
End If
End Sub
#Region "Context Item Handlers"
Private Sub Item1_Click(ByVal sender As Object, ByVal e As EventArgs)
MsgBox("You clicked 'entry1'")
End Sub
Private Sub Item2_Click(ByVal sender As Object, ByVal e As EventArgs)
MsgBox("You clicked 'entry2'")
End Sub
#End Region
End Class