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Just a shop that can follow an install guide. Most people that work on german or British cars should be able to figure out the MINI, not that hard. Most VW/audi shops could do it, just give them a heads up and do you have the install pdf?
There is nothing special about them. Any competent shop that can do brakes won't have a problem. I did my own last spring, it was quite simple, I was expecting it to be worse.
Agree with GPMini - I installed mine a couple of years ago. No big deal. You need to be prepared to bleed the brakes though, so have brake fluid on hand. A pressure bleeder is also a big help - check out ECS Tuning, I have their Schwaben brand bleeder.
If you're not up for DIY, then find an independent shop you trust.