Although it is a bit of an uphill battle, it is absolutely NOT impossible to specialize in neuropsychology when your program does not offer coursework in it. You must seek out external practicum experiences where you will be provided with the training. Make sure that your supervisors are involved in the neuropsych community, and if possible, try to go to sites where the supervisors are board certified (ABPP). You did not mention which year you are in, but if you are just starting out, make sure that you can get as many practicum experiences as possible in neuropsychology - I am trying to pursue a career in neuropsych so 2/3 externships aka practicum experiences were in neuropsychology, and the other one was 50/50 - rehab/neuropsych. My internship has a heavy dose of neuropsych as well.
You aren't barred from the world of neuropsych if your program isn't known to produce neuropsychologists, but make sure that you can show to others that you truly are interested (via hands on experiences and research).
Good luck!