The Alleghenian Orogeny was formed due to the colliding of North America and Africa.
The Carboniferous Period was a gap in New York's rock record, as the rocks have been weatehred away; the only place where you could possibly find rocks from the Carboniferous Period are at the border of New York and Pennsylvania, somewhat near Jamestown. You could find conglomerates, sandstones, and shales there.
North America was near the equator during this time due to plate tectonics, so New York State must have had a much warmer climate than it did today.
The NYS Rock Record had Carboniferous Rocks as Bedrock (specifically during the Pennsylvanian Period).