Think it was after the 1848 Revolutions. The Sicilian deputation offered him the crown, but Genoa was absent and by the time he had returned from his army manoeuvres the sìtuation had changed.
Oh you are right, it was Duke Ferdinando of Genova (VE II's younger brother), for some reason I was thinking about an earlier time period...
There might be an opportunity for him to become King of Sicily, but only in the framework of a Sardinian victory in the First War of Independence and, even then, it would be a longshot. Anyways, that would mean an Italian confederation of sorts, not certainly the Two Sicilies taking the lead in the unification effort.
If in 1820 the King hadn't asked for Austrian intervention at the Congress of Laibach, given how Britain only agreed with extreme reluctance it is posible that a Constitutional government could have lasted, but it is very difficult. It would already be quite difficult to do in Sardinia, with a Carlo Alberto who at the time was in one of his liberal times, with Ferdinand and Francesco it is almost impossible, especially considering how I don't think the Carbonari would accept a more moderate option (like extending Sicily's 1812 Constitution, which sort of copied the Westminster system) rather than their preferred monocameral Spanish constitution.
Probably the only opportunity is a surviving Murat dinasty, this would have a good chance in the 1848 equivalent.