Cyrus's middle initial is W in census records. I found Walter as his middle name on a family tree at Rootsweb's Worldconnect (Claire White's).
In the Federal Census of 1900, Cyrus & Clara are living at Red House, Cattaraugus Co., NY. They have two sons, Roland (Robert?) & Lewis, and are living next to Cyrus's parents and a cousin.
According to cemetery data at NYGenweb, this couple had a son Roland 1897 - 1913. Possibly he was a twin to Robert (?).
In 1920 the family is living at Salamanca, Cattaraugus Co., NY. The names of the 7 children are difficult to decipher.
In 1930 the family is at Red House again: Cyrus W. 50, Clara B. 50, Cyrus W. 20, Harry E.13, and Alice 79.
From findagrave.com: "Cyrus Remington . . . helped build the Aleghany State Park in NY. His name is on a plaque in the visitors' center."