Hello! Our knowledge of the internal/political histories of the various Phoenician city-states remains limited to the extreme; even regnal chronologies are impossible to establish with any precision (though hordes of scholars have wasted time and ink trying to do just that). Outside of Carthage, the most famous Phoenician figure is probably king Hiram [I?] of Tyre, whom the Bible (namely 1 Kings) mentions in relation to the reign of king of Solomon of Israel and the building of the First Temple in Jerusalem. Additional information comes from the first-century AD Jewish historian Josephus, who quotes (or so he claims) now-lost Greek translations of Tyrian records, mostly in his polemic Against Apion. Many scholars are inclined to believe in their authenticity--they otherwise wouldn't have a source for Tyrian history!--and there's no compelling reason in my mind to suspect forgery. I've discussed and quoted these passages in another post, if you're interested.

Another famous Phoenician is king Pygmalion of Tyre, who presided over the foundation of Carthage sometime in the late-ninth century BC (I recently concluded that the traditional date, 814/3 BC, is probably wrong). Of course, the story involves his sister Elissa, later to become "Queen Dido" in Vergil's Aeneid. I've also discussed this topic in a separate post.

And that's about it. King Ethbaal [I?] of Tyre appears in the Bible, and a jumble of Phoenician rulers are named in other sources without much detail. If you do not include Carthage, I would politely recommend that you choose a different topic, as there is simply too little evidence to adequately reconstruct the life or reign of any individual Phoenician. With Carthage, however, we do have plenty of Greek and Roman sources for the careers of Hannibal Barca and, to a lesser extent, his father Hamilcar. I hope you find this helpful! :)

Edit: If you want an example of the challenges involved in determining the identities and chronologies of Phoenician rulers, take a look at this article.