Then Eire has a whole mess of other problems*, which the famine actually helped with (in a rather brutal way). However, there is likely no mass migration to the US (which was only running at ca 20k pa), but rather a steady trickle to Australia instead.
Irish independence was born in New York City, and they'll be no Fenians ITTL. That perhaps has implications for the ACW, with no ready source of mercernaries the Union is harder pressed, and maybe losses. No Fenians = no push for Canadian Federation (hence no Australian Federation).
* Mainly no primogenure (sp?) meaning that the lands of the common farmer kept getting divided into smaller and smaller plots, and the health of the population deteriorated.