5V Arduino and 12 led's power options
There are a few different calculations you can do that will help figure this out.

Energy consumption

The first is how much power you'll need to run the system. Each LED has a voltage drop of 2.0 V. Assuming you run the LEDs at their maximum current (20 mA), they'll each use 2.0 V * 0.020 A = 0.040 W. For 12 LEDs, that's 480 mW, assuming the rest of your system is perfectly efficient. In an hour, you would use 480 mWh, or 0.480 Wh.

As a first estimate, let's say your system will be only 50% efficient, so you need 2 * 0.480 Wh (roughly 1 Wh) to run for an hour. (You can probably do better, but we'll get to that.) A CR1225 coin cell is a 3 V battery rated for 47 mAh. That's the same as 3 V * 0.047 Ah = 0.141 Wh. That's about 1/7th of what you need, so your LEDs will last around 1/7th of an hour, i.e. 8 or 9 minutes, with one CR1225 coin cell.

Efficiency

Can you do better than just guessing 50% efficiency? Sure.

It depends on how you wire the LEDs and what current-limiting resistors you use. You could make 6 strings of 2 LEDs each and run them off of a 6 V pack made from two coin cells in series. Each string would have a 4 V drop, so you'd need to drop the remaining 6 - 4 = 2 V over a resistor. At 20 mA per string, that's a 2 V / 0.020 A = 100 ohm resistor.

In this case, 1/3 of your power would be dissipated in the resistors (since 2 V is 1/3 of 6 V), so your efficiency would be 66%.

You might try 4 strings of 3 LEDs with no ballast resistors, but I suspect that their brightness would drop off quickly as the battery voltage sagged. Your efficiency would be 100%, but the brightness would suffer.

You could also try running off of the 5 V supply you mentioned; with the right resistor, you could hit 80% efficiency.