How outdoorsy are they? There are heaps and heaps of great walking tracks out west. Much cheaper than clay bird shooting and go carts too.
Mountain biking at
Woodhill Forest? (You can hire bikes out there.)
My cousins used to do
archery in their school holidays?
I know you can do clay target shooting at Waitemata Gun Club on Old North Rd (out the back of Kumeu) but don't know if they have a website sorry.
If you want a break drop them off at
Youthtown 
(schedule for 13-16 year olds
here, you do need to book them in though)
Rock climbing at Birkenhead Leisure Centre or Extreme Edge in Mt Eden?
Paintball, only it's pricey.
Is Laser Strike passe these days?
Found
this page when I tried to google for the gun club page