I'm most familiar with the River Division (Weehawken NJ to Albany NY) of the West Shore during the period of first generation diesels, roughly the late 1940's to the early 60's. Generally speaking, commuter and passenger trains were handled by Baldwin RS-12 and Alco RS-3 roadswitchers, freights were hauled by Alco cab units (FA-1 and -2s, FB-1 and 2s), and Alco S unit switchers worked the yards. I've seen photos of RS units working local freights and I'd venture a guess that the Alco cabs were the primary power for freights to Buffalo, but the Central had a huge diverse fleet of locomotives so other makes and models undoubtably made appearances.
The road locomotives were painted in the Central's classic lightning stripe paint scheme (black carbodies with gray stripes outlined in white). Yard locos were all black with white lettering. The commuter passenger cars transitioned from green with yellow/gold lettering to gray with white lettering during this period.
George Elwoods fallen flag site has many photos of these locomotives http://www.rr-fallenflags.org/nyc/nyc.html
and Morning Sun's "Lightning Stripes Volume 2" dedicates many pages to the River Division including ferry service to Manhattan.
Other folks will need to chip in if you're looking for info on a different time period.