This is one way how such a Property could be made - integrate it into the Code of your Control (Form) and replace the Button with your UserControl ...
<System.ComponentModel.DesignerSerializationVisibility(System.ComponentModel.DesignerSerializationVisibility.Content)>
Property ButtonProperties As Button
Get
Return myButton
End Get
Set(value As Button)
myButton = value
End Set
End Property
Private myButton As New Button