The Madeira Regional Archives has enlarged its databases with judicial proceedings which include 19,262 crime and civil suits from 1790 until 1973. I decided to search it to see if any of my ancestors were listed in it. I went to the advanced search and chose Nossa Senhora da Piedade for the parish. I did this because this was the church where christenings occurred in. This search resulted in no results.
I tried again but with Porto Santo as the parish. This search found 18 items, none of which were my family. I will have to check in on this database to see if there are updates.