You might be able to save yourself a whole lot of hassle by simply hiring a pet sitter to take care of your animals while you're in Costa Rica. There are a lot of extra obstacles to navigate when traveling internationally with pets, and it's up to you whether or not these troubles are worth the effort. That said, taking an animal on a Costa Rican vacation can be one of the best experiences you and your furry friend will ever share.
When bringing dogs and cats on board, you absolutely need to have up-to-date shots. Your vet should know which immunizations they will need in order to travel, and if they don't, then you should probably consider getting a new vet. You will need certification and paperwork proving that the shots were administered less than 30 days ago. Even one day over may bar your pets from travel.
Costa Rica used to bar the importation of birds but have recently lifted this ban. However, you cannot export birds from Costa Rica, so if you're just visiting, you'd better hope your bird knows the way home. Best said, leave the bird at home!
There will be periods of time known as blackouts where absolutely no pets will be transported by a given Airline at all. Pay attention to these blackout periods so that you know when you can and cannot travel with your animal friends.
Costa Rica is famous for beautiful beaches, and packs of loose dogs that roam the streets. If your animal is nervous around these types of creatures, then you may want to consider a pet sitter.
Any international travel guide worth reading will tell you that bringing pets overseas is difficult, but if you just can't stand to part from your cat or dog for an extended period of time, what else is there to be done? If you can't imagine taking a trip to Costa Rica without your pet, look into airlines that are very pet-friendly and try to book pet-friendly hotels ahead of time.