I hope you are still researching William & Eliza Carson.
I believe our Williams may be one in the same; I have William in Stillwater as of the 1870 & 1880 censuses. Their son, Charles married Mary Agnes Cronin, daughter of Jerry & Ann Holleran Cronin (Richfield Springs, NY).
Please reach me at firstname.lastname@example.org
if you care to pursue an exchange of info.