Thank you so much for these interpretations. This has been very helpful.

I have checked Freebmd and I think it looks like his wife died in this area too and that her full name was Christina Luigia Amodeo.
For 'Requietorio' translate I got requietory, which might mean sepulcher. (Sorry, I have just noticed I added a slightly different word in post 1 so I have now amended)
So might a rough translation be along the lines of...?
'Memorial of Luigia Amodeo, forty four years old, taken from the loving care of Alessandro, her husband, she received the blessing of rites before returning to God on 12 April 1878.
Also, on 9 December 1880, Alessandro Luigi Amodeo suffered a fatal fall down a compartment hold whilst working on board .. and his blessed soul was taken to the Lord. He was a maritime Captain since 52.
Reunited with his Luigia, he leaves behind brothers and a sister, Gabriele, Pietro and Lucia in Trieste to mourn him and ask for these loved ones to receive eternal peace.'