Exactly what are you looking for in a tire? It makes a big difference what your objectives are. If you're looking at the PS4S, that's a excellent performance tire in dry and wet conditions.
The X2 is a tough vehicle to purchase tires for, due to the unicorn size of the standard 225/40R20 94Y XL tire. I have yet to see any other tire of that size available other than the OE P ZERO RUN FLAT (PZ4). I can't imagine what the engineers at BMW were smoking to select this tire and this tire size. I do not like these tires at all, due to the harsh ride (run flat) and the noise and it's hard to understand why they would select a tire that was sole source. I regret not checking this before I order the vehicle, or I would have ordered the 19" wheels instead. I will be shopping for a 235/35-20 when it's time to replace the OE tires and it will not be a Pirelli, at least if I can help it.
I have Michelin PS2 on the front of my M3 and Continental ExtremeContact DW on the rear. The PS2 handle well, but they don't last very long (especially on the rear
). The PS2 was replaced by the PSS. They are excellent tires, but they are going out of stock, replaced by the PS4S, which is even better than the PSS. The Continentals are wearing okay, but they have very soft sidewalls, so the back-end of my car is unsettled with them. I would have put Michelin PSS on the back, except at the time, they were not available in the size I wanted (285/30-19) except in run flat, which was a show stopper. Continental has since come out with a new tire called the ExtremeContact Sport, which is on par with the PSS.
If you're planning to downsize to 19", get a wider wheel so you can comfortably fit a 235 width tire on it (e.g., 8.5"). That will result in a wider selection of available tires, but be careful of the offset. To maintain clearance with the suspension, you need to move the tire outward, just don't get carried away.
If you go for 225/45-19, PS4S and the Continental ExtremeContact Sport are available. I wouldn't go to 18". Due to the tall tire, you need a 50 series tire to maintain the diameter, which will kill the handling, as you have found.