There is probably a web of "Largey" who immigrated - if I post some other snippets you might be able to work out all the links to see if they are relates to each other. I realise this is not the family you were asking about.
Noticed a passenger list for a Henry Largey born Belfast 1899 and travelling on the Carmania arriving 19 November 1920 - he was 21 years old - father was Patrick Largey, 6 Sydney Street,Belfast. This Henry was going to cousin Hugh Toal, 528 North 5 th Street, Harrison NJ.
This chap could possibly be the one who married Margaret Tolan and lived on Elm Street Kearny, Hudson, New Jersey in 1930
Margaret A Tolan 54
Mary Tolan 26
Margaret Largey 25 Born Norrhern Ireland. Married at 23 years. Imm 1921. NA.
Henry Largey 29 Born Northern Ireland. Imm 1920. NA. Driver Ice and Coal Business. Son-in-law Married at 27 years.
Mary Largey 22 Born Northern Ireland. Single. Lithographer.
Thomas Largey 25 Born Northern Ireland. Boarder. Imm 1929. Body Assembler. Automobile Plant.
Ambrose Largey 27 Born Northern Ireland. Boarder. Imm 1929 Body Assembler. Clerk. Retail Grocery.
William J Pollard 21
Leo P Morrizay 28
John Graham 35
This was also the chap Shelly quoted on the death record for May 1976 in reply 2
This was the Largey family of Sidney Street
http://www.census.nationalarchives.ie/pages/1911/Antrim/Court/Sidney_Street/135706/Sandra