TheFork users who ate in Tirrenia have said really good things about La Locanda, Osteria da Simone and Ristorante Pizzeria Barbarossa. Maybe you should give them a try!
Some of the more popular American Express restaurants where you can go with your pets in Tirrenia according to TheFork users include:
La Locanda, with a 9 rating
Osteria da Simone, with a 9.2 rating
Ristorante Pizzeria Barbarossa, with a 8.1 rating