Quarantine permit for dogs???

Nothing in the local news suggests that the requirements for importing a dog have changed.

First, the dog must have been vaccinated against rabies at least 30 days before the travel date but not more than one year before that date. The "30 days before travel" requirement is because the incubation period for rabies is 30 days. Costa Rica only recognizes 1-year rabies vaccination.

Then, the vet who vaccinated the dog must complete an International Health Certificate which attests to the dog's state of health. That Certificate must be counter-endorsed by a member of the "veterinary service". If you're not familiar (who is?), the "veterinary service" is an arm of the U.S. Department of Agriculture. Their offices are located in every U.S. state and at least some large cities. The veterinary service must endorse the International Health Certificate within ten days of the travel date.

The dog must travel on the same plane as its owner or be consigned for travel by a licensed animal transporter.

The airlines each have restrictions on traveling with live animals and they're very strict. You must make arrangements with the airline in advance and follow their restrictions.

Since the dog will be handled as "cargo", Costa Rican Customs will charge an import duty of 25% of the cost of transporting the dog. You'll have to deal with Customs at the airport when you arrive. Bring cash.

If you find this all very daunting (we did), there are internationally-licensed animal transporters who do this for a living and know all the ropes. Nobody said "cheap".