Wanting to stay for 3 months. Would one rent for that long
YES, they would rent you one for that long, but it would cost you a LOT.
if I were you...I would locate the town you want to stay in.
Then you can find either a used car dealer in that town and work a deal or it is possible a nearby town will have rentals that would be MUCH cheaper than anything you would find ONLINE or near San Jose.
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Life is short...so get out of the Rat Race and Enjoy Paradise in Costa Rica.