There is a formula for capacitors some what like Ohms law:-
Q = VC
Where Q is the charge in coulombs, V is the voltage in volts and C is the capacitance in Farads.
One amp is a charge of 1 coulomb flowing past a point in 1 second.
So to find C you need to rearrange it to say:-
C = Q/V
For 100mA over two minutes you get:-
0.1 * 60 * 2 = 12 and at 12 V you get 12 / 12 = 1
So the total energy stored in the capacitor is equal to a 1 Farad capacitor. In fact that is the total energy and you can't run anything once the voltage drops below 7V so that actually reduces the time.
Now you can get super caps at this sort of value but the current density of these are limited, that is you are limited to the charge / discharge currents you can actually get.
Conclusion:- I would forget about capacitors and have a small rechargeable battery in the circuit.