I'm not sure what sort of joystick you're using, but you can get a simple analog one working without much work.

I use some hall effect ones in this keyboard:

https://github.com/sffubs/dactyl_manuform_gimbal

They are analog joysticks, so generate a voltage that indicates the position. The joystick code is in here:

https://github.com/sffubs/qmk_firmware/blob/master/keyboards/handwired/dactyl_manuform_gimbal/dactyl_manuform_gimbal.c

Unfortunately it's not too well organised, but it just does an analogReadPin to get an X/Y value, scales it to the desired mouse values, and sends it using a pointing_device_task.

I am a big fan of joystick pointing devices, would love to see what you end up making!