Gioia,
At 120 ohms and 1 ampere you will require a source >120 V and you will have a power dissipation of at least 120 watts. If you use standard linear circuitry at 0.5 A, you will have 30 W in the coil and >= 30 W in the regulator. If you use the same 120 V source for the 9 ohm coil the power in the regualtor at 1 A will be >= 111 W. None of these requirements are difficult to meet, but if you are not aware of them, you may get more smoke than you like!
I would probalby start with power op amps by Apex. I think they were bought by someone else a few years ago, so it might take a bit of searching to fiond them. Some of their devices can handle the magnitudes of voltage and current that you require. You can use a standard current regulator circuit with the power op amp. To reverse the polarity, you can use an analog switch IC controlled by one of the digital outputs to switch the op amp configuration between inverting and non-inverting. The USB-6259 spec sheet says the range is -5 V to +5 V, so you may not need a polarity switch.
Lynn