public Form1()
{
    InitializeComponent();

    // Form that has a button on it
    button1.PreviewKeyDown +=new PreviewKeyDownEventHandler(button1_PreviewKeyDown);
    button1.KeyDown += new KeyEventHandler(button1_KeyDown);
    button1.ContextMenuStrip = new ContextMenuStrip();
    // Add items to ContextMenuStrip
    button1.ContextMenuStrip.Items.Add("One");
    button1.ContextMenuStrip.Items.Add("Two");
    button1.ContextMenuStrip.Items.Add("Three");
}

// By default, KeyDown does not fire for the ARROW keys
void button1_KeyDown(object sender, KeyEventArgs e)
{
    switch (e.KeyCode)
    {
        case Keys.Down:
        case Keys.Up:
            if (button1.ContextMenuStrip != null)
            {
                button1.ContextMenuStrip.Show(button1,
                    new Point(0, button1.Height), ToolStripDropDownDirection.BelowRight);
            }
            break;
    }
}

// PreviewKeyDown is where you preview the key.
// Do not put any logic here, instead use the
// KeyDown event after setting IsInputKey to true.
private void button1_PreviewKeyDown(object sender, PreviewKeyDownEventArgs e)
{
    switch (e.KeyCode)
    {
        case Keys.Down:
        case Keys.Up:
            e.IsInputKey = true;
            break;
    }
}