I have the Emirates NBD card, which dumps a few tier miles in my account every month. Seems like it's for spend on Emirates tickets. I can never exactly reconcile the amount -- probably given for the base fare (no taxes, etc.) but I never bothered to look closely.

It used to be possible the get the card even if one wasn't a UAE resident, but I don't think that's an option anymore.

It's conceivable that there are other card options but probably not convenient for the OP. Look like a trans-Tasman tier run might be your best option.