I think a lot of people who want to learn English will be happy to pay a native speaker for conversation practice. You don't really need a formal teaching method to do this. You just listen to them speak and correct their pronunciation and grammar as you go along. Even though these people live in a country full of native speakers, many of them are too shy or lack the opportunities to practice with native speakers. If you were to volunteer, your time, you would have a lot of takers.
As for teaching in Italy, find some Italians where you live, help them with their English, and have them record a short video testimonial (in Italian) about how you helped them improve their English. Compile these testimonials into a video that you can post online. This a great marketing tool.
"Leila helped me improve my English so much! I highly recommend her! Thanks Leila!"
Testimonials like this will help you find private lesson work in Italy.