There are a couple of ways to do this ...
Nice and simple is to select the control and send it the down key ...
dateTimePicker1.Select();
SendKeys.Send("%{DOWN}");
but there is always the faint danger that the sendkeys may go elsewhere if you have a "clicky" user.
Safer way is to send the message directly to the control
using System.Runtime.InteropServices;
...
[DllImport("user32.dll", SetLastError = true)]
private static extern int SendMessage(IntPtr hWnd, uint Msg, int wParam, int lParam);
const int WM_SYSKEYDOWN = 0x0104;
at the top of your class and then after your messagebox
SendMessage(dateTimePicker1.Handle, WM_SYSKEYDOWN, (int)Keys.Down, 0);