It would be hard, undoubtedly: Irish nationalism goes back a long way. One thing that would help a LOT is if Pitt the Younger was able to secure Catholic Emancipation in 1801 as part of the Act of Union, as was his intention. Unfortunately George III in OTL was against Catholic Emancipation because he viewed it as being in violation of his coronation oath to protect the Anglican faith (exclusively).
If pulled off properly, this could perhaps set up the idea that "England/Britain mistreated Ireland when they were separate, but when the two joined, the Irish were finally treated as equal to mainland Britons'. Wouldn't get rid of Irish nationalism altogether of course, but that's probably your best bet for keeping the British Isles united under a single state.