I do not know anything about the specs of the FPGA in question. But all driver circuits for logic signals I know can handle up to 24mA (sometimes 48mA) of current. In source mode, i.e. if you just use the output pin, this current is available at a minimum output voltage of around 2.8V, or, in other words, the guaranteed minimum output voltage at maximum current load is around this value. As FPGAs usually are not designed to drive high current loads, and as 50mA would be far too much for most dedicated driver ICs I have serious doubts whether your circuit will be able to handle this.
Usually it is better to connect high current loads in sink mode, i.e. connect the load between +5V (or the supply voltage of the output driver, whichever is lower) and the output. In this case you can get an output voltage very close to the supply voltage at full current rating - but again, the current ratings I know are 48mA maximum.
In any case, when connecting any inductive load (i.e. anything which contains a coil) to electronic circuitry you should add a diode in parallel with the coil, connected with the catode to the higher potential, to breakdown reverse current which occurs when an inductive load is disconnected from the supply.