I am researching William Stanion and his wife Jane. He is listed in the US census of 1860 as a paperhanger living in New York,born around 1820 in "GB & Ireland". Their son Stephen,born around 1837 is listed a born in NYC. If these data are correct. William and Jane must have emigrated young, either separately or together. If together, the imminent arrival of Stephen may be a cause.
As far as I have been able to ascertain, the name stems from the village Stanion in Northamptonshire. Most instances of the name I have seen are either in that county or in the neighbouring Leicestershire and Cambridgeshire. Huntingdonshire would fit neatly as well.
There is a Anthony Stanion who emigrated to Massachusets in ab. 1634. This line does not seem to be closely connected to mine.
I have found a few isolated instances of marriages in the 18th century, ie Robert Stanion, born in Easton Maudit, married Elizabeth Langley on 26 Mar 1748, Orlingbury, Northamptonshire, England and Richard Stanyan , born in Higham Ferrers, Northamptonshire, England, married Frances Langley on 19 Jun 1743, Great Harrowden, Northamptonshire, England.
Don't forget to check the spellings Stanian and Stanyan as well.