I think you have to come up with multiple PoD's that prevent the demand for Home Rule becoming so strong, for a start have Pitt face down George III over his opposition to Catholic Emancipation as part of the Act of Union. If you can then have Ireland, and not just Ulster, industrialise more intensively in the following years creating a prosperous Catholic merchant class who will see their interests served by being in the Union just as the Ulster Protestants did. This will also create a demand for more workers in Irish cities meaning less people living in extreme poverty in the rural areas. You can also have measures to protect the rights of tenant farmers from summary eviction.
Above all you need to either prevent, or more realistically, reduce the impact of The Great Famine as it was the feeling that Britain hadn't done enough to help that really pushed Home Rule up the agenda. Peel's Government carried out a series of relief measures that was helping the situation but after Russell won the 1847 election he, under the influence of Trevelyan, ended those measures and that was when the death rates and the numbers of emigrants really shot up. So you need Russell to over rule Trevelyan and maintain the relief, also there was a famine in the 1790's when the Government blocked food exports so as to provide relief. The same measure wasn't carried out in The Great Famine and the idea that Britain let Ireland starve out of hatred remains a potent one in Irish Nationalism.
So if you can show the ordinary Irishman that the Union "works for Ireland" then you could potentially prevent the groundswell of opinion in favour of Home Rule ever developing.