Among these candidates, we find several recently extinct species:
The Puerto Rican Sloth (and its ilk) were prevalent throughout the West Indies until 3,000 to 4,000 years ago. Ranging from 10 - 30 lbs, possessing a "spiny" coat, and mostly arboreal, this sloth in many ways fits some descriptions of the Chupacabras.
Large rodents, collectively known as Hutias, were also prevalent throughout the Caribbean. The largest of these rivaled in size that of a North American black bear. These larger ones were long since lost to the fossil record, but smaller specimens - around 15 pounds and about the size of large cat - existed until the inception of the Spanish Colonial period. Most of these species resembled the capibara, the largest extant rodent known to science. Still even smaller Hutias, which are still larger than your average rat, are hunted for food on nearby islands such as Cuba. Hutias aren't currently known to exist on Puerto Rico, but if any relic species of these echimyidae, or spiny rodents, - in whatever size - still existed in hidden enclaves throughout the island's remoter corners, then perhas this could explain sightings as well. This spiny fur, coupled with their oddity and arboreal proclivities would, too, fit witness descriptions.
Currently, I am working on examining further these creatures and others as possible explanations for what we now term as the Chupacabras, and will publish much of these reports, as well as other tales, in a forthcoming work on the mysteries of Puerto Rico. This volume will be similar in format to that of Strange State and will likely be available through cafepress.com.