These two maps show the correct route from San Jose to Nosara and Liberia to Nosara. Be aware that some GPS products are extremely erroneous and should not be trusted.
Driving directions from Liberia International Airport to Nosara, Time 2 hours
This is the quickest and safest route to Nosara. That said the last hour from Nicoya to Nosara should not be driven at night and few do. There is a Hilton Garden inn accross from the Liberia airport that has a shuttle to and from the airport. The only place to get anything to eat along this route is in Nicoya. There is a restaurant just outside the entrance to the Liberia airport to the left 200 meters almost next door to National Car rental.
Driving directions from San Jose International Airport to Nosara, Time 4-5 hours.
There are two ways out of San Jose that join up at the coast. The Trans American Highway, AKA the old road and the new toll road. The new road is greatly prefered. Your rental car provider will have the direction on how to get to the new road.