Depends what you mean by Ireland.
The Irish Republic was proclaimed in the Easter Rising 1916 and was formally established three years later by the extra-legal parliament Dail Eireann. The Irish Republic was never formally recognised by Britain. Langer is actually right - Russia was the only state to recognise the Irish Republic and tried without success to get the nations of the Versailles Peace Conference to follow suit, but to no avail.
If you mean in the period after the War of Independence, then as co-signers of the Anglo-Irish Treaty (1922), the United Kingdom would have been the first to recognise the Irish Free State as a self-governing entity.
In 1937 the country adopted a new Constitution and became a sovereign state (known as Ireland or Éire). Again, the UK was the first to recognise Éire (but not with the name Ireland), and was careful to state that it only recognised newly sovereign Ireland as consisting or the territory which had made up the Irish Free State and did not recognise Ireland's territorial claim to the six counties of Northern Ireland. The USA was second to recognise Ireland.
In 1949 Ireland declared itself fully a republic (Republic of Ireland Act 1948), leaving the British Commonwealth, ceasing to be a dominion, and formally replacing the British monarch with an elected President as head of state. I don't believe there was any formal recognition of this as it did not affect Ireland's diplomatic or sovereign status. On the day that the Act came into force (18 April 1949) King George VI sent his congratulations to the first President of Ireland, Sean T O'Kelly.
As far as I know this is right - I am happy to be corrected by a real historian.