Low resistance digital potentiometer - alternatives?
It took a while to get over the confusion you caused calling a meter a motor.
With the type of meter you have (it's a differential current meter), the two coils are used to maintain accuracy when the supply voltage varies. In your vehicle the voltage may vary from 10V or less cranking through to above 14V when charging. 

Note that your particular type of meter is NOT driven by a constant current, so any answer that pushed toward that as a solution is wrong. The current through your meter varies both with supply voltage AND the 'sender' resistance value.  

Your idea of using multiple resistors to create a replacement for the 'sender' is not a bad one. However you will need more bits than you imagine. 

I assume that instead of a resistive sender you are going to use an MCU with some appropriate sensor to measure the fuel level ….you just want to use this conventional style meter to display the results from your MCU.

You should use FETs to turn on the individual resistor values to get the appropriate resistance value you need. 

A circuit such as this may suit your application:







simulate this circuit &ndash; Schematic created using CircuitLab

Note here that I show AO3400 FETs with very small RDS(on) even when driven by a 3.3V MCU.

Even with 8 bits from the MCU or S/R the resolution around 120 Ohms is only 3 bits, but it's very easy to implement.