As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.
There are no census websites for Italian census that I am aware of. In the central/south census' are usually taken locally and maintained in the local anagrafe office. It is not really a census, more an update of your personal record on file, spouse, address, occupation etc. Parish Churches did their own form of census over the centuries but you have to go to the individual church to access it. Some towns still have an old form of census called Foglio di famiglia, or Registro del Popolazione but again, it is only accessible locally and has not been microfilmed.
I have searched in many churches and the priest is the key. If he is interested he will look up the record, if not the letter will sit in the in basket. If there is a parishioner who is capable of looking up the record he will be asked to do so. Since you really want a family tree, one or two records will not be enough and to keep writing just serves to annoy an already busy priest. I would write a letter in Italian if possible asking the priest if there is someone in his parish who could search the parish records on your behalf. Offer to pay the person AND offer a donation to the church for their cooperation. Do not send money initially but do include an self-addressed envelope. Your payment should be based on the amount you might expect to pay for these certificates in your own country. It is unlikely they will provide photocopies as the documents are fragile and usually stored in the damp, humid church office. You might also include a pedigree chart with the information you have already printed on it. Don't give them everything, just the starting point for them.