Alright, we all know genoa ends up being an awesome civ, at least on viceroy and monarch.
Most of the production might that comes from them stems from an early settlement of sicily and early conquer of tunis (for me at least). Because of these two mixed with hanseatic league to feed those hard working miners, they make an awesome combo to build wonders, armies, and settlers.
Unfortunately, Genoa never seems to capitalize on these two. Whenever I play another civ, they are weak, settle Corsica and Sardinia which are alright. And NEVER get Tunis or Sicily, although I've Genoa settle very near to Tunis before. They end up always being behind in techs and often dont get Milano for hundreds of years, let alone other italian cities. I know this may not be historically accurate but its necessary to the balance of the game - Africa is NEVER settled!!!
They should have motivation to build sicily and tunis and conquer more italian cities, because right now they are really not living up to their full potential