Parkerizing, or rather phosphatizing of gun steel did not happen until 1918 or 1919 when Springfield Armory first used it to finish/refinish US Military arms. Previous to this, rust bluing was the standard finish in both military production and commercial arms.
Since your NY State militia rolling block rifle is parkerized, it is a safe bet that it was done at least 50 years after Remington made it. I can't imagine that parkerizing was done by or for the military since it was long obsolete by the adoption of the M1892 Krag, and the M1903 Springfield.
I would suspect one of the surplus arms dealers, possibly Bannerman of New York City would have something to do with the refinishing.
John