Moore Family

I have hit a brick wall with my gg grandfather Alexander Moore b 1841 somewhere in Ireland to a John Moore and Elizabeth. His siblings are Ann b 1833, Elizabeth b 1836, John 1839, Mary 1843 and Catherine 1845. Both John and Elizabeth were born in 1804 and moved to Liverpool sometime between the birth of Catherine and 1851 as they appear in Liverpool i the 1851 census. In the 1861 census I found Alexander said to have been born in Sullylish Co Down Ireland.
I have searched the maps and can not find a Sullylish in Co Down