You don't give any dates of birth, but I did find the following at the Ellis Island One Step Search Site:
Surname / First Name / Last Residence / Age / Birth Year / Emigration Year
Carrol, James Bessbrook, Ireland 23 1887 1910
Carroll, Bernard Bessbrook, England 26 1897 1923
Carroll, Daniel Bessbrook, Ireland 20 1900 1920
Carroll, Frank Bessbrook, Ireland 24 1889 1913
Carroll, Mary Bessbrook, Ireland 22 1889 1911
The record for Bernard shows his address as 31 Hill Street, Bessbrook; names his wife, Alice, as his next of kin at home. Bound for a friend, John Matthews, Hotel Majestic, New York.
Daniel gives his mother, Mrs. Carroll, Derrymine, Bessbrook, as his next of kin. Bound for his brother, James, in Chicago.
James names his father, William, Derryware(?) Bessbrook as his next of kin and he is bound for a friend, Jno. Costello in Chicago.
Frank (Francis) gives his father, William, of Derrymore(?), Bessbrook as his next of kin. Bound for a friend, Michael McAllister, Providence, Rhode Island.
Mary gives her mother, Mrs. A. Fitzgerald, 25 Hill Street, Bessbrook, as her next of kin. Bound for her husband, Daniel Carroll, in Chicago.
I think this is one of the families in the 1901 Irish Census:
Surname, Forename, Age, Sex, Relation to head, Religion
Carroll, William, 33, Male, Head of Family,Roman Catholic
Carroll, Anne, 33, Female, Wife, Roman Catholic
Carroll, James, 13, Male, Son, Roman Catholic
Carroll, Francis, 11, Male, Son, Roman Catholic
Carroll, William, 9, Male, Son, Roman Catholic
Carroll, Catherine, 7, Female, Daughter, Roman Catholic
Carroll, Bridget, 4, Female, Daughter, Roman Catholic
Carroll, Daniel, 2, Male, Son, Roman Catholic
The same family in 1911 census has additional children, Edward, Patrick, Mary, Vincent.
Not really sure how or where Bernard fits in.