I looked into it and a Cadillac CTS from 2008+ uses a 5x120 bolt pattern same as the Paceman/Countryman. Size is right, it has a 135/70/R18 tire on it.
Price was right at the auto recycling near me at $50, so I went and picked one up.
Looks good, fits in the hatch flat, not under the cover of course, but flat and the hatch closes.
Went to test fit it in the rear and the center hole is just a bit too small to fit over the hub on the Paceman. Not a show stopper, I can grind the edges off a little bigger, maybe measure it out and use a hole saw so its neat and even. For a spare at $50, it seems like it should work well enough.
Pics:

The tire. Not bad for $50

So close. Did a little grinding with the dremel there but it wasn't aggressive enough. Will get something with more bite or a hole saw should do it ok, its only aluminum.

fits in the hatch decent enough. hatch closes no problem.

 

Did some checking, and the Mini wheel center bore is 72.6mm vs 66.9mm for the Caddy CTS.
72.6mm works out to 2 55/64" so round that up to 56/64 which reduces to 7/8 so Ima get a 2 7/8" hole saw to make this work nice nice


edit: I guess I could have just said get a 73mm hole saw too lol

 

5.7mm difference sounds more than it looks like on the picture, but I wonder how are going to make sure the hole saw is dead center?

 

If you look at the pic of the back, where its in my hatch upside down, the center bore hole is tapered, so it should center itself when it gets down to 73mm in the taper pretty easily and as long as I go slow.
I'm not too concerned with that as the lug bolts hold the tire on, the center bore hole just needs to clear the ring on the hub.

 

I see. Never done this myself so was just curious. Sounds like an interesting project

 

k, I got my 2-7/8 hole saw and put it to work. Man, this kind of sucked as that big a hole saw is a little bit of weight on a hand drill. There was a bit of wobble so I had to go slow. I smoked my old HF orange corded drill :( I had that one for a while too. I got most of the way through the wheel, and it was enough to fit it up. Fits fine. Clears everything. Will work as a spare for sure.
I'll probably get another HF drill and go a bit more on it eventually, the hub on the other side could be a little deeper so to be sure I can clear that. Not too bad a project, would have been nice to have a drill press to run this on, would have been smoother for sure. As the 73mm is a little bigger than 72.6mm there is a little expected play to line the bolt holes up, once you get the 1st one started the rest line up easy. Might 3d print a spacer for the .4mm difference, but its not a real concern as the bolt pattern matches and it all fits good. I did not try it in the front, seems enough clearance it would work there too if you needed it too to get to a better area or off the highway, but others say always put the small spare on the back and move a back tire to the front if you get a front flat.
So for $50 for the spare, and $10 for the hole saw, not too bad. I might say just get a 3" hole saw as they are more common and easier to get, not a big difference either way.


2-7/8 hole saw is slightly bigger than the hub center

Using the hole saw on the drill was a bit of a pain, it wobbled and I had to go slow. The hole is probably a little bigger than 2-7/8 cause it wobbled so much.

Fits swell after the hole gets opened up. I didn't drill al the way through here, but deep enough the wheel sat flat against the rotor. I might later after I get another cheap drill

 

Congrats! I think I wouldn't be brave enough to try it without drill press

 

I probably could have done something with a wood block or a 2x4 clamped to the other side of the wheel that the middle bit would have centered on pretty easily, but I wasn't smart enough to do it that day. Will do it for sure if I get another drill and have at it again to make it just a little deeper
But its nice to have spare after getting rid of the run flats for $50, and a hole saw.

I'm sure it can be done cleaner, so consider this a proof of concept or a starting point at least, that shows the factory CTS/CT6 spare is a good option to start with.
Maybe start with a 72mm hole saw, then ream it out to 72.6mm? This would go quick for anyone with machine shop access too. But it also works the way I did it (minus 1 smoked HF corded drill :( )