This is not a good UI practice - hence why it's hidden and not easy to change.
Derive a new control from Button, and use SetStyle to allow them both:
public class MyButton : Button
{
public MyButton()
{
SetStyle(ControlStyles.StandardClick | ControlStyles.StandardDoubleClick, true);
}
}
You must enable both styles for double click to work.
Then you can add the button, and manually add the event handler:
MyButton mb = new MyButton();
mb.Text = "My Button";
mb.Size = new Size(100, 30);
mb.Location = new Point(100, 100);
mb.Visible = true;
Controls.Add(mb);
mb.DoubleClick += MyButton_DoubleClick;
You can't add the handler via the Properties pane in the designer, as it's a hidden event.