I don't see how the Ottomans would figure they could expend resources on such a far away venture so late. Like literally on the other side of Great Britain. They had enough business going on in Romania and Serbia, had to watch out for Growing Persians, and deal with an increasingly independent Egypt. All they did against Napoleon was forgotten by the west at this point, evident by French and British encroachment in Africa. And honestly, what would support for the Irish really do? The Englishman would be sitting there laughing, that the Irish wanted to cause trouble. But perhaps Greenland, owned by the defeated Danes, could be given to the Turks as a prestige holding (that they assuredly knew the maintenance would be too much for the Turks to handle, and it'd be a cheap buying game between Atlantic powers), but turned out to be profitable through well invested fishing industries, ensuring its longevity as a Turkish territory, who also helped educate others of its native Inuit culture. During the potato famine, Ireland becomes the #1 importer of fish produced in New Cyprus.