I am trying to find information on Sarah Coulter who came to America about 1875 and eventually married Simeon Josiah Parker (about 1890, I think). They had many children including my grandfather, Walter Parker, b about 1908. I am trying to find information on her parents, siblings, etc.

Do you have the marriage record giving her age at marriage and / or father's name ?

To locate her on the census, will need more information about a possible birth year and/or father's name

The first census in which I find her for certain is the 1900 US Federal Census which gives the following information:

Name: Sarah Parker
Home in 1900: Maynard, Middlesex, Massachusetts
Age: 26
Birth Date: Jan 1874
Birthplace: England
Race: White
Ethnicity: American
Immigration Year: 1875
Relationship to head-of-house: Wife
Father's Birthplace: Scotland
Mother's Birthplace: England

Also on the census it states that they have been married for 10 years (1890), which would have made her about 16 at the time of her marriage.

I cannot find the immigration record. That's all that I have. I have not written to the State of Massachusetts for a marriage record yet. That might give more information.