This family is DNA linked from Cheryl Nichols, sharing 116 cM over 5 segments. Finally found the link in the Nichols tree to connect it to Henry Johnson.
This is also based on census analysis for 1820-1840 in which two females are born between 1825 and 1830. Emma would be one of them.
This family is living next door to Richard Johnson, son of Henry and Henry Johnson, Jr. in 1870. Her parents are both born in New York listed on 1880 census. She is a widow in 1900, living alone.

Connection to Homer Balcom:
The Buffalo Courier, Tuesday, 5 April 1892, viewed at http://fultonhistory.com
WESTERN NEW YORK
Niagara County
Wilson
Gilbert Adams and wife have returned from an extended visit with their daughter, Mrs. Homer Balcom, in Buffalo.

1850 New York, Niagara County, Wilson, stamped page 510 or 1019 (taken 30 Jul 1850)
dwelling _16, family 486
Gilbert Adams, age 25, male, carpenter, born Canada
Emma ———, age 19, female, born Canada
Wm H.———, age 1, male, born Canada
[last 2 are not correct, both born in New York]

1860 New York, Niagara County, Wilson, p. 3 (taken 14 Jun 1860)
dwelling 22, family 22
Gilbert Adams, age 35, male, seaman, $200 real estate, $100 personal, born Canada
Emma ———, age 29, female, born New York
William ——-, age 10, male, born New York
Henry ———, age 8, male, born New York
Catherine —-, age 4, female, born New York

1865 New York State Census, Niagara County, Wilson, 1st Election District, p. 54 (taken 30 Jun 1865)
137 visitation, frame house, $300, family 128
Gilbert Adams, age 39, male, born Canada, married once, currently married, fishing
Emma Adams, age 35, female, wife, born Niagara, mother of 4 children married once, currently married
William Adams, age 15, male, child, born Niagara, single
Henry Adams, age 14, male, child, born Niagara, single
Catherine Adams, age 8, female, child, born Niagara, single
Fred Adams, age 2, male, child, born Niagara, single

1870 New York, Niagara County, Town of Wilson, Ridge Road Post Office, p. 63, stamped page 644 (taken 6 Sep 1870)
[This is the same page as Henry Johnson, Jr. family and Richard Johnson family]
dwelling 527, family 534
Adams, Gilbert, age 45, male, white, grocer, real estate $800, personal $400, born Canada
———, Emma, age 39, female, white, keeping house, born New York
———, William, age 20, male, white, sailor, born New York
———, Henry, age, 18, male, white, sailor, born New York
———, Katie, age 12, female, white, attended school, born New York
———, Fred, age 6, male, white, attended school, born New York

1875 New York State Census, Niagara County, Town of Wilson, p. 49 (taken 5 Jul 1875)
visitation 472, frame house, $100, family 475
Gilbert Adams, age 50, male, head, born Canada, married, mechant [sic]
Emma Adams, age 45, female, wife, born Niagara, married
Katie Adams, age 25, female, daughter, born Niagara, single
Willie Adams, age 25, male, son, born Niagara, single, sailor
Henry Adams, age 23, male, son, born Niagara, single, sailor
Fred Adams, age 11, male, son, born Niagara, single

1880 New York, Niagara County, Village of Wilson, E.D. 194, p. 23?A, stamped page 404 (taken 19 to 21 Jun 1880 by Lynford LeVan)
Harbor, dwelling 84, family 86
Adams, Gilbert, white, male, age 54, head, married, carpenter, born Canada, father born New Hampshire, mother born Canada
———, Emma, white, female, age 50, wife, married, keeping house, born New York, parents born New York
———, Fred, white, male, age 17, son, single, at home, born New York, parents born New York [sic]
———, Henry, white, male, age 28, son, married during census year, sailor, born New York, parents born New York [sic]
———, Alice, white, female, age 22, daughter-in-law, married during census year, boarder, born New York, father born Canada, mother born Ireland
Wilson, Orin, white, male, age 68, [blank], widower, boarder, born New York parents born Massachusetts

1900 New York, Niagara County, Wilson Township, Wilson Village, E.D. 94, sheet 6B (taken 12 Jun 1900)
Harbor, dwelling 156, family 162
Adams, Emma, head, white, female, Apr 1830, age 70, widow, mother of 7 children, 2 living, born New York, father born Pennsylvania, mother born New York, farmer