How would I change the border color of a button?

I am not sure what sort of application you are working on, however in winforms there is no border property for a button directly on it, even in the designer. You can use a flat style button. And your type will have to be button.

you can do it like:

buttonName = "btn" + y.ToString() + x.ToString();
Button btn = this.Controls.Find(buttonName, true)[0] as Button;
btn.BackColor = System.Drawing.Color.Blue;
btn.FlatStyle = FlatStyle.Flat
btn.FlatAppearance.BorderColor = Color.Red;
btn.FlatAppearance.BorderSize = 1;

Unfortunately, this will only work on button with a FlatStyle.