Hard to say what's typical souvenir of Genoa. Basically, it can be anything and everything, as long as it presents Genoa and its sights (like the Lighthouse, for example, that is the symbol of this city, I guess). The best place for tourists to get their souvenirs is the Aquarium in Porto Antico: there are many shops that sell souvenirs and what a choice of things they have! Just to name few:
bags, pictures, photo frames and photo albums, pots, mugs, kitchen gloves, spoons, plates, egg-stands, fridge magnets, aprons, table clothes, pillows, lighters, ash-trays, key-rings, clocks and watches, books, notebooks, sculptures, figures, ship replicas, coasters, T-shirts, soft toys, dolls, pens, posters, thermometers, bibs for babies, bottles, rings, cards, tins, bells...
...and many more :)
More souvenirs from other beautiful places all around the world:
jane, ladybug-zen, ian, bonnie, esti, sophie, cele, modsquad, caitlin, joyce, ani, couturecoucou, kim, a day that is dessert, natsumi, epe, kaylovesvintage, trinsch, c.t., jeanette, outi, schanett, ritva, dongdong, francesca, state of bliss, jennifer, dana, denise, cabrizette, bohemian girl, ruth, dianna, isabelle, amber, all the lovelies, mister e, janis, kari, jgy, jenna, skymring, elizabeth, audrey, allison, lise, cate, mon, victoria, crescent moon, erin, otli, amy, ida, caroline, lisa, dorte, kimmie, la luna dans le ciel, nicola, malo, vanessa, britta, virgina, april, rebecca, b, sunnymama, kyndale, samantha, karen, kristina, angelina, juanita, pamela, emily, dorit, sophie, janet, mcgillicutty, desiree, travellingmama, aimee, mirtille, madchen, guusje, boise, daan, woolie, 2ndspring, jenell, tina, inna, lisa, ninja, ibb