From Goa Gokarna is 3 hours away. From Gokarna murdeshwar is 1 hour away. So totally you need 5 hours to cover both spots from Goa. Yes there are lot of transport centers who offer inter state self drive cars. You can check with Zoom cars. Also check with justdial.
Sorry could not find self drive transport centers. Many travel tourist houses are ready to offer a car with driver but self drive is only within Goa. So my suggestion would be drive within Goa, but if you are planning to visit Gokarna and murudeshwar it’s better to hire a car with a driver.
I have already contacted several self driven car rentals, no one is providing self drive car outside goa. Even in zoom cars it is shown that car rental is only restricted for goa roaming not outside goa. Thats the reason why i am posting this question. Would be helpful if you know any particular car rental that will provide inter-state rental.
Appreciate and thank you everyone for your suggestions. I have contacted many self drive car rentals in goa and none is ready for giving/providing a self drive vehicle for outside-goa-rides, strictly restricted to roam in goa only. The second option ZOOM CARS website it is mentioned like RTA imposed some rules that the vehicles that are been booked from zoom cars should also be taken and considered for GOA-ROAMING-ONLY. A rental car with driver is the suggestion they are giving me. Hope this helps to anyone who have the same query.