I have not made any connections yet to my Mariah Butler but have found the following people in Allegan Co. Census records.

Most likely Mariah was related to William since they both were born in Newark
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Mariah Butler b.March 16, 1827 in Newark
d. October 16, 1906


1840 Census ~ Allegan Township .. William G Butler (Newark)

1850 Census ~ Allegan Township... William G (50), Emily G (40) and James G (10)

1860 Census ~ Allegan Township... Augustus S, (born Allegan), Emily (born Allegan), James (Newark Townshp), Minerva (Cascounty Township). William A (Cascounty Township)

1870 Census ~ Allegan Township...
August (35...Banker born NY), Cornilia (36...born NY), Wolcott H (5... born Mich), August S Jr. (2...born Mich)

1870 Census ~Hopkins Township... Charles (28..born Mich), Mary M (23...born Pen), Lydia A... (3...born Mich)
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Jacob and Mariah (Butler) Moomey's children were born in OHIO per census records. Mariah was also born in Newark

Mariahs family must have settled in OHIO

1860 Census ~ Salem Township
Jacob Moomey 42 (b Penn), Maria 32 (b Newark), Simon 16 (b Ohio), Sophiona 14 (b Ohio) , George 12 (b Ohio) , Lewis 10 (b Ohio) , Ezral 8 (b Ohio), Albert 5 (b Mich) , Emeline 2 (b Mich), Olive 5/12 (bMich)