Ireland was part of the United Kingdom in the 1800s - from the 1st of January 1801, to be precise. So the currency was that of the United Kingdom. The basic coins were as follows:

2 farthings (1⁄4d) were worth 1 ha'penny (1⁄2d)
2 ha'pennies were worth 1 penny (1d)
3 pennies were worth 1 thrupenny bit (3d)
2 thrupenny bits were worth 1 sixpence (6d)
2 sixpences were worth 1 shilling (1s)
2.5 shillings were worth half a crown (2s6d)
2 half-crowns were worth a crown (5s)
2 crowns were worth a half-sovereign (10s)
2 half-sovereigns were worth a pound note (£1, or sometimes L1) - but a coin called a sovereign had the same value
1 pound and one shilling were worth a guinea.

There were also two-guinea, two-pound and five-pound coins, though not in common use, and a few oddities like third-farthings and half-farthings, mostly in use in the Colonies (and they probably would not have been accepted in Ireland).

The actual prices of goods in Ireland the 19th century varied widely, particularly during the years of the Great Famine, 1845-1852, so you'd be best off looking for contemporary newspaper ads or price lists to get that kind of information.

(EDITED for formatting.)