As I understand it:
1. If your car is older than 8 years old, you can enter Senegal with a CDP. However, it might not be stamped at the border, you might have to go to St Louis or Dakar within 48 hours of crossing the border to stamp it there
2. If your car is older than 8 years old, and you do not have a CDP, then you will have a difficult time.
3. If your car is less than 8 years old, you can get a Paissez Lavant at the border.
That is my understanding, maybe other people can tell us differently?