So? Use the Random class:
private Random rand = new Random();
private void button1_Click(object sender, EventArgs e)
{
DateTime randomDate = new DateTime(rand.Next(1066, 2188), rand.Next(1, 13), rand.Next(1, 32));
}
You will probably want to add some error checking, as this will throw an exception on 31st April and so forth, but otherwise it will generate a random date in the years 1066 to 2187 inclusive.