Everything is possible, nothing is easy.
How much of the system do you have? Do you have the transmitter, receiver and joystick? The joystick could just be a switch that operates an up/down counter like the 4510 CMOS. You would most likely use serial data, so you need a shift register, altho you could do 4 bit parallel data by using subcarriers in your transmitter. You either need to transmit the clock along with the data, or use Manchester coding.
The reciever, after assembling the data in parallel format, could operate a digital potentiometer which varies the pulse width of a switching supply that drives the motor.