I believe you are referring to Diodorus book V, 19-20, where Diodorus recounts the Phoenician discovery of a wooded, fertile island.

Now, I will preface my answer by saying that I am not a Greek historian, and am not particularly aware of the current state of scholarship relating to Greek histories, so if someone more knowledgeable comes along and corrects me, I accept that critique.

All right, so if we assume that Diodorus is telling the truth, the island he refers to must be located off the coast of Africa. The land of "Libya" that he refers to covers all of North Africa, and he mentions after discussing this island in book V chapter 21:

But since we have set forth the facts concerning the ocean lying off Libya and its islands, we shall now turn our discussion to Europe.

This seems to indicate clearly that the island in question is off the coast of Africa. We know the Phoenicians sailed the waters of the Atlantic, they founded the city of Cadiz on the Atlantic Spanish coast, and had colonies on the corresponding African coast. The description of being blown out to sea could absolutely be true, and is feasible.

It certainly isn't North America however. There are many blogs and websites out there that allege that the Phoenicians sailed to North America, but they couldn't have done it in a matter of days. There's no material evidence of Phoenician occupation in the New World whatsoever.

So where is this referring to?

Scholarly consensus seems to indicate one of the islands of Macaronesia, perhaps Madeira or the Canary Islands. Dr. Glenn Markoe, a very well-respected scholar, indicates that Madeira is the place Diodorus referred to. He's not the only scholar who believes the Madeiras are good candidates for this island, as DB Harden also opines that it is a good candidate in D. B. Harden (1948). The Phoenicians on the West Coast of Africa. Antiquity, 22, pp 141-150.

So it appears that scholarly consensus puts Diodorus' island among the Macronesian islands off the coast of Morocco and Western Sahara, most likely Madeira or the Canary Islands. Unfortunately, as far as I am aware, there has been nothing conclusive recovered archaeologically from those islands to establish a Phoenician presence, though I am also unfamiliar with any archaeological investigation into that question.

If you give me the exact reference to the Diodorus passage (i.e. book and chapter, or, if you have a translation that does not mark these, then the name of translator, publication year, and page) I can check academic commentaries in the library tomorrow. I don't remember Diodorus well enough to recognise immediately what you are referreing to. The Greek and Roman authors love telling stories about far-off places where Carthaginians sailed to the extent it's almost a trope; most of these accounts have a rather dubious truth value. The only island I can think of on the spot is the Sherbro Island which is where academics believe Hanno the Navigator sailed. We know of his expedition from the only piece of Carthaginian literature that has (kinda) survived to our date, through a mediocre Greek translation of an inscription detailing the journey that Hanno supposedly hung up in the temple of Ba'al in Carthage, known as the The Voyage of Hanno, commander of the Carthaginians, round the parts of Libya beyond the Pillars of Heracles, which he deposited in the Temple of Kronos. I know that Herodotus and Pliny the Elder at least mention Hanno's journey, so I guess Diadorus could be talking about Hanno's expedition, but I'd need to get the passage to check.