I'm not sure if you know this, but Italy has had a very robust national system of vital records (called Stato Civile) in place since about 1865:
It is based on the system Napoleon put into place when he invaded/conquered Italy in the early 1800s. Once Napoleon was defeated in 1815, most areas of Italy stopped the civil record keeping but not all - southern Italy (formerly the Kingdom of Naples and the Kingdom of the Two Sicilies) kept using the system, and Sicily began using a similar system in 1820. So for places like Nicastro, which is in the State of Catanzaro and was part of the Kingdom of the Two Sicilies, they should have civil records going back to the early 1800s. Currently, I think records older than 75 years are available for release to the public.
Of course, these records are all on paper. One copy of each record is generally held in each town where the act is recorded and another was filed with a regional court and later transferred to the state archive. But the LDS church and the Italian Ministry for Cultural Heritage and Activities have been working with the state archives to film these records and many of them are now online, either at FamilySearch or at the Italian "Antenati" site. You're in better shape than most folks who have Italian ancestry if you already know the exact town they came from.
Currently, Nicastro records for births for 1809 and 1823-1857 and deaths from 1832-1851 are available online. These can be accessed on the Antenati site or at FamilySearch (but only at an LDS Family History Center or a FamilySearch Affiliate Library). I think FamilySearch may have some additional documents listed in the catalog for Nicastro but again, you can't access these with a regular internet connection.
FamilySearch and Wikitree both have information on how to use/read/translate the Stato Civile records.
Most of the online records have not yet been digitally indexed so you have to look through year-by-year. However, many registries have an annual index either in the front or the back of the volume. It is mostly handwritten so sometimes there's an art to interpreting the script.
If you want to find a record that isn't available online, your best bet is to try to contact the town Stato Civile directly. Some will answer by email but you should write a letter for your first contact for best results. It would need to be in Italian. There are examples floating around the internet of how to write the letter. I think since the late 1960s Nicastro has been folded into the city of Lamezia Terme. Here is the page where they give information on requesting a copy of a birth certificate (atto di nascita).
BTW, in addition to Stato Civile records, the Catholic Church has maintained baptism, death, and marriage records since the 1500s. Again, each individual church maintains its own records. Very few of these have been scanned so you would need to contact a church directly to locate a particular record.