Is there a simple way to add a border to Kivy Buttons

You may want to look at the border property of the Button Class,basically: In kiv:

Button:
        border: (10,10,10,10)

I believe this will be the border image used by BorderImage

Disclaimer: Not tested but its along those lines

I suppose you mean additionnaly to the current background/border.

If so, you probably want to use some canvas instruction.

You probably want to add them in canvas.before so it's drawn before the text of the button.

The instruction you'll use will depend on the effect you want, but Line is probably a good start.

Button:
    text: 'test'
    canvas.before:
        Color:
            rgba: .5, .5, .5, 1
        Line:
            width: 2
            rectangle: self.x, self.y, self.width, self.height