Thanks for the replies, that John Hickey is definitely a good possibility.
The other siblings born in Ireland unfortunately don't seem to appear on there, but if anyone has any other ideas they were:
Mary born about 1847
Daniel born about 1851
James born about 1851 (twins according to the 1861 census)
Patrick born about 1854
After finding another tree on Ancestry and checking a few records, it looks like Mary married Joseph Theobald. Like John (well, the one that seems most likely to be the correct one), following her family through the census records shows she was from Bandon, Ireland.
I've ordered both marriage certificates as everything seems to fit. They should confirm their father as Daniel Hickey and therefore Bandon being the right area.
What would be the next step? Are there likely to be records in Ireland that aren't online?