Prior to visiting Puerto Rico, I had read that the coqui is a ubiquitous nocturnal noisemaker throughout the island, but upon arrival, I learned two important things. First of all, I learned that it isn't ubiquitous, and that there are places where the micro-beasties don't exist. Secondly, I learned that most travel writers are lazy as hell and don't bother to do their own research… which of these is more important to you?
The Coqui, which you can read all about on Wikipedia, are a unique genus of frog, with perhaps ten species represented. They make a noise unlike any mammal or insect you've ever heard. Birds might match it, if they were so inclined, but it sounds more like a car alarm being set to deter criminals from violating your rented Rento.
Everything I had read in advance said that, no matter where you go throughout the whole of Puerto Rico, you'll always hear them chirping away all night, but I'm here to tell you, with locals to back me up, that this just isn't the case.
It shouldn't matter much, since you'll stay where you'll stay and visit where you'll visit, but in the event that it somehow matters so much, even from an academic standpoint, they don't blanket the entire island.
The coqui love wet weather, and in the south of Puerto Rico, specifically in the arid areas of Gúanica to the west of Ponce, the climate is simply too dry to support the chirping critters. So if it matters that much to you, and it shouldn't, head to the area around the dry forest of Gúanica and count on never hearing so much as a single one of them… well, except once the rainy season rolls around, but this isn't a big tourist hotspot, the south in the rainy season.