The Mahaffy family were said to have emigrated from co. Armagh, Ireland to Ontario, Canada, prior to 1841.
The first known are James Mahaffy who married Sarah McLaughlin in 1841.
All information from Dale Mahaffy:

Due to possible privacy issues, any person born 1900 and later are presumed to be living unless an actual death date is known or approval of inclusion is given to me; a husband, wife, or issues are noted but no names and/or dates are provided; if anybody can supply updated information, please leave me an e-mail and I will update. Note: (09) etc, are generation numbers and are calculated from my generation (15)

Changes for the month will be made in red and will remain until the end of that month.

(11) James MAHAFFY [c.1813-1887] m.1841 Sarah McLAUGHLIN [bap.1817-    ]
   |----(12) John MAHAFFY [1842-1926] m.1873 Mary Ann HUTCHINSON (McHENRY) [1846-1928]
   |        |----(13) Nelson MAHAFFY m. Mattie HOPWOOD
   |        |----(13) Maude MAHAFFY m. Austin DILLING
   |        |----(13) Fanny MAHAFFY
   |        |----(13) Sophie MAHAFFY m. David HENDERSON
   |        |----(13) Sarah E. MAHAFFY [c.1875-    ] m. Dan LINTON
   |        |----(13) George MAHAFFY [1877-    ]
   |        |----(13) Mary L. MAHAFFY [1878-     ] m. Robert NORRIS
   |        |----(13) Edith A. MAHAFFY [1881-1968] m. Joseph LINTON
   |        |----(13) Leassa (?) MAHAFFY [1883-     ]
   |        |----(13) Emma MAHAFFY [1886-    ]
   |        | ---(13) Myrtle MAHAFFY [1892-    ]   m. Robert MacLEAN
   |----(12) James MAHAFFY [c.1845-1930] m.1877 Ellen MILLER [1852-1922]
   |        |----(13) Ella M. MAHAFFY [1888-1909]
   |        |----(13) Sarah A. MAHAFFY [c.1879-    ]
   |        |----(13) Selina Edith MAHAFFY [1879-1979] m.1906 David HODGSON [1872-1913]
   |        |----(13) Ethel MAHAFFY [1886-1969] m.1909 William SPARKS [1884-1963]
   |        |----(13) Margaret [1892-1968] m.1946 Ross TAYLOR [1900-1995]
   |----(12) William MAHAFFY [1846-1926] m.1882 Mary Ann (Annie) KANE [1855-1931]
   |        |----(13) William Charles MAHAFFY [1883-1905]
   |        |----(13) Freeman Gibson MAHAFFY[1884-1955] m.1917 Margaret Helen (Nellie) DALRYMPLE [1886-1968]
   |        |----(13) John Thomas MAHAFFY [1886-1961] m1.1912 Emma Elizabeth Amelia KAHLE [1885-1948]
   |        |    -----   John Mahaffy m2. Mae McBRIDE
   |        |----(13) Alice May MAHAFFY [1887-1984] m.1917 Irvine AIKENS [1887-1977]
   |        |----(13) Annie Louise MAHAFFY [1889-1959] m.1914 Franklin Wilson HARRIS [1889-1962]
   |        |----(13) George Franklin MAHAFFY [1891-1918]
   |        |----(13) Norman Lessly MAHAFFY [1893-1974] m.1920 Margaret Jane McALINDEN [1894-1986]
   |----(12) Elizabeth MAHAFFY [c.1852-    ] m.1873 Robert W. McGLOCKLIN
   |----(12) Samuel MAHAFFY [1852-     ] m1.1877 Emma JOHNSON [1853-180]
   |       |----(13) Emma Louise MAHAFFY [1880-1954] m.1906 Herbert PARRISH [c.1878-1940]
   |      ----   Samuel MAHAFFY m2.1880 Eliza WILSON [1852-    ]
   |----(12) Mary Jane MAHAFFY [1855-1929] m.1879 John G. MILLER [1844-1932]
   |        |----(13) George James MILLER [1879-1980
   |        |----(13) Sarah Agnes MILLER [1881-1961] m.1920 Eustace H. PAYNE [1875-959]
   |        |----(13) John James MILLER [1883-1965]
   |        |----(13) William George MILLER [1884-1965] m.1912 Mary DOW [    -1959]
   |        |----(13) Thomas Mathew MILLER [1886-1942]
   |        |----(13) Margaret Jane MILLER [1889-1965]
   |        |----(13) Mary Elizabeth MILLER [1891-1964] m.1917 Ernest Samuel TEMPLEMAN [1891-1960]
   |        |----(13) Lillie Isabelle MILLER [1895-1951]
   |        |----(13) Samuel Gibson MILLER [1893-1894]
   |----(12) Thomas MAHAFFY [1855-1932] m. Annie FRANCIS [1861-1923]
   |        |----(13) James Herbert MAHAFFY [1883-1961]
   |        |----(13) Tamina Alice MAHAFFY [1885-1885]
   |        |----(13) Thomas Wilbur (Wib) MAHAFFY [1886-1944] m. Mary DALRYMPLE [1888-1979]
   |        |----(13) John Alexander MAHAFFY[c.1887-1888]
   |        |----(13) Frederick G. MAHAFFY [1889-1996]
   |        |----(13) Alexander F. MAHAFFY [1891-1952] m1. Unkown m2. Evelyn UKN [    -1959]
   |        |----(13) Mary Olive MAHAFFY [1895-c.1980] m. Robert HOGGARTH
   |----(12) Gibson MAHAFFY [1860-     ] m1c.1882 Sarah Ann LINTON [1857-1887]
   |        |----(13) Effie M. MAHAFFY [1883-1970] m. Harry PECK [1879-1970]
   |        |----(13) Leslie E. MAHAFFY [1884-1906]
   |        |----(13) Ella L. MAHAFFY [1886-c.1978] m. Jack McNIVEN
   |     -----   Gibson MAHAFFY m2.1889 Martha Matilda LINTON [1864-    c.1944] (sister to Sarah)
   |        |----(13) Albert W. MAHAFFY [1889-    ] m. Florence UKN
   |        |----(13) Vera L. MAHAFFY [1892-1984] m.1919 William GATENBY
   |        |----(13) Harvey G. MAHAFFY [1893-1971] m1. Beulah UKN   M2.1945 Margaret BAYNE [1904-1983]
   |        |----(13) Lindsay MAHAFFY [1895-1983] m.1919 Minerva FYKE
   |        |----(13) Harry F. MAHAFFY [1897-1978] m.1924 Ella Blanche FYKE
   |        |----(13) George Clifford MAHAFFY [1899-c.1940]
   |        |----(13) Edgar Earl MAHAFFY [1900-c.1914]
|         |----(13) Stanley MAHAFFY [c.1903-c.1978] m. Jerry UKN
   |----(12) Sarah MAHAFFY [1860-1869]

**** We are not certain of this family but it does make sense as one of the children is named after a grandmother's maiden name and Nelson -not a common Christain name - is not unfamiliar in the McLaughlin family.