I have a gold mirror and like the style but not the gold. Does anyone have any ideas on what to use to update it. I've been told to rub black shoe polish on it to tone it down.

You do mean that the frame itself is gold, painted or gold leaf?

If there is a wrapped or back edge to the frame, try some experimenting there. If not, then use the sides, top, bottom outside edges to check different techniques. (if you do not like the results, it could be painted over solid black, if you could not get it wiped off)

Guess I would consider what type of look I was trying to achieve? Might try some of the shoe polish on the side and see the result?

I was able to disguise a shiney brass light fixture by sponging on a cream colored paint. Tiny spots of the brass are still visible among the mostly cream color sponging, and I left them on purpose. Not very noticeable but tends to add just a hint of sparkle/depth to the paint coat.
I also used liquid airbrush paint, just because it covers so well, and yet is a very thin coat as opposed to acrylic craft paint (thicker bodied). But you can try what you have.