To rent one, no. There is a company in Manuel Antonio that rents them out as well as a new one in Uvita that does tours. My friends have done that and they're not licensed. Just like you don't need a motorcycle license to ride a quad in a tour. Quads are registered as motorcycles. The police don't hassle Tourists much. Do a search of "Jet Ski Manual Antonio" etc and visit their site.
Most quads/bikes are illegal anyway. Stay off the pavement. Owning a jetski is a waste of money and a high risk for theft. They're not really a big thing here. Rent one if you feel the need to 'ski.
Not sure what a quad is, but my question is, are motor scooters legal? I wouldn't ride one in San Jose, but would they be practical transportation in a small town?
You'd need a motorcycle license for a scooter. Doubt you'd be stopped tho. It depends on where you are. Small town with paved roads, sure but the rainy season could be an issue. A small town with dirt roads full of boulders and holes, not so much. I doubt the suspension would be adequate. My old town had many 70+ yo ladies driving illegal quads and loving it.
Best advice is to ask around when you get here. What do others do. If you're the social type you can find a shopping group and make an event out of it. I picked up a lot of hitch hikers both locals and gringos. Cars are always broken here so there's a network of possibilities.