The link you found is for the state archives but Cosenza Province is not included in the database. Records in Cosenza are difficult to find on-line. Do you have access to a local FamilySearch facility? They have microfilm records yo can view.

Cristina, Cece is right, you should go to the comune office of the Anagrafe. They are usually open in the morning M-F but you can search on-line for "anagrafe" for the comune and you might get specific hours.

Don't expect English but in Tuscany they might speak some. Have copies of your information ...

Angela,
My wife's Nigro ancestors were from Laurenzana, on the other side of the mountains from Grumento Nova.

Di dove la sua famiglia origine in Italia? Mia moglie ha parenti Nigro origine di Basilicata.

Yes that is for her marriage on 21 Jan 1901
Spouse looks like Nicola M. Flammia of Marciano