Proper cold-brew coffee works much better for this, IMO.
I've devolved to instant coffee for this, and not even good stuff, just the cheapest instant coffee at Costco. It is purely for the caffeine, though, but a bit of coffee-ish flavor is nice too.
Also, I don't like the idea of just chilling hot-brewed coffee? But if I did, aeropress would probably be a good way to do it, sans an espresso machine.