If the car has a 10 or 12" spare wheel then you can fit a Group 34 battery in the standard battery box. you might need a 34F which has the posts reversed if your positive battery cable won't reach the battery post.
www.HeritageGarage.com
2005 Mini Cooper replace car battery. Alternative to MINI part
a good light weight factory type battery would be the mini cooper battery or the CSL m3 battery
The 2014 MINI Cooper has double overhead cam (DOHC).
The 2002 MINI Cooper has single overhead cam (SOHC).
The 2010 MINI Cooper has double overhead cam (DOHC).
The 2009 MINI Cooper has double overhead cam (DOHC).
The 2013 MINI Cooper has double overhead cam (DOHC).
The 2004 MINI Cooper has single overhead cam (SOHC).
The 2008 MINI Cooper has double overhead cam (DOHC).
The 2011 MINI Cooper has double overhead cam (DOHC).
The 2005 MINI Cooper has single overhead cam (SOHC).
The 2003 MINI Cooper has single overhead cam (SOHC).