The transition from free labor to enslaved labor was an unthinking decision that took place hundreds of years prior to the 19th century, but since you are asking about the 19th century I will do my best to answer. For starters there weren't enough Irish to fill the labor demand, the famous Irish diaspora didn't start until only a few years before the American Civil War and there were only about eight million Irish in all of Ireland anyway ( as opposed to four million slaves on the eve of the civil war). The Irish also predominately immigrated to the Northern states because there was more work, it was a more favorable climate, it was cheaper, and there were established Irish communities in Northern cities. Some planters after the revolution did try to use white labor usually with lacking results. James Monroe brought on a number of German indentured servants in the 1810's to work on his Ashland-highland plantation, his overseer reported that they were lazier than the slaves and they ran away eventually anyway. Which brings up another problem, white workers can leave at basically any time even if under an indentured servitude contract with little feasible recourse for rather obvious reasons. Without diving deeper into the free labor vs enslaved cliometrics or how deeply ingrained slavery was into every aspect of the South, there are numerous practical reasons why Irish workers were not feasible.