Well, potentiometers are NOT the way to do it (not directly anyway)
There are various circuits which allow you to create a variable current source, but I'm not sure that you'll save an awful lot more space over a small power supply.
There are options if you're willing to go switch-mode, but that would have more ripple and thus more variation of the magnetic field. This may not be suited to your experiment.
If you're driving your 0.8 ohm load at 2.5A, it will drop 2 volts. If your constant current source is operated from 5V, then the peak dissipation is only 7.5W which is easily handled.
This page shows the basic circuit for a constant current sink. In this case the constant current flows between +12V and the drain of the mosfet. (He's not using it for that purpose exactly). Note also that the circuit is powered by a split power rail (+12/-5V). The current is given by the voltage at the non-inverting input of the 741 divided by the sense resistor.
In your case, the sense resistor could also be the coil! In any case, I would place a reverse biased diode across the coil to remove any chance of problems due to its inductive nature.
The Mosfet will need a heatsink, and it would be preferable to operate it from a lower voltage (say +5V)
Note that this means you'll need 3 voltage rails, +12, -5, and +5. (the -5 could be anything between -5 and -12 without causing problems) Only the supply to the drain (+5 in this case) needs to supply significant current, but the regulation of the +12V supply needs to be good as this is also a reference for the current limit. If you wish to monitor the current, do so in the drain of the mosfet.