Between Goa and Kanyakumari, a rather long distance for a car ride is about 1230 km, or about 19 hours one way. If there is time, then such a trip will be an exciting, but tedious journey. But it's better to choose the route by train or by plane.

If you take the train from Goa from the station of Margao (code MAO), you need to select a suitable train to Trivandrum station (TVC code). In Trivandrum, you need to change the train to Kanyakumari Cape station (another 3 hours). Or from Trivandrum you can take a taxi to Kanyakumari, drive about an hour. Transplanting with a train trip can also be made at Kollam (QLM) or Thrisur (TCR). Indian Railways website - enquiry.indianrail.gov.in

On the plane you will need to make a flight from Goa to Trivandrum. But there are no direct flights, only with a stop, for example, in Chennai (Madras) or in Bangalore.

Good luck!