Having the right spigot rings is essential otherwise the wheel simply doesn't locate properly. Just make sure they are the correct internal diameter for the MINI.
If you're certain you've got the correct rings and you still have a wobble, find yourself a tyre specialist who can balance the wheels using finger plates which locate the wheel on the balancing machine using the stud holes and NOT the centre hole of the wheel. This is because the centre hole is not necessarily accurately machined and the "cones" that most tyre shops use don't locate the wheel correctly.
Yeah, I know it's a bit anal, but believe me - it works...!!
Try your nearest Pirelli Performance Centre:
www.pirelli.co.uk/en_GB/tyres/dealer_list/pirelli_performance_centers/ppc_gb.jhtml;jsessionid=LUDA330YQEHOHFYKJOPSFEY
- any of these guys have the kit and the expertise to sort out your problem.