Клик по кнопке осуществлять не при попадании курсора в ее область, а в область картинки на ней

    // This method will change the square button to a circular button by 
    // creating a new circle-shaped GraphicsPath object and setting it 
    // to the RoundButton objects region.
    private void roundButton_Paint(object sender, 
        System.Windows.Forms.PaintEventArgs e)
    {
 
        System.Drawing.Drawing2D.GraphicsPath buttonPath = 
            new System.Drawing.Drawing2D.GraphicsPath();
 
        // Set a new rectangle to the same size as the button's 
        // ClientRectangle property.
        System.Drawing.Rectangle newRectangle = roundButton.ClientRectangle;
 
        // Decrease the size of the rectangle.
        newRectangle.Inflate(-10, -10);
        
        // Draw the button's border.
        e.Graphics.DrawEllipse(System.Drawing.Pens.Black, newRectangle);
 
        // Increase the size of the rectangle to include the border.
        newRectangle.Inflate( 1,  1);
 
        // Create a circle within the new rectangle.
        buttonPath.AddEllipse(newRectangle);
                
        // Set the button's Region property to the newly created 
        // circle region.
        roundButton.Region = new System.Drawing.Region(buttonPath);
 
    }