You need to search for your family in the "Registro Civil," now called "Registro Demografico" for Orocovis. They should have records from 1885 to the present. You also may be able to get information from the local catholic church in Orocovis.
The Mormons, also known as the Church of Jesus Christ of Latter-day Saints, have microfilmed many of the church and civil records for Puerto Rico, among other places, and they make these records available to anyone thru over 3,000 of their Family History Centers which can be found around the world.
Here is a link to their web page where you find a location near you and also see what microfilms they may have for Orocovis:http://www.familysearch.org/Eng/Library/FHC/frameset_fhc.asp
Tony Rivera Maldonado