All manned stations have carts that will carry passengers and their carry-ons to the train, you just have to ask.
That is not quite true.
Most stations with checked baggage have carts to the train, but I can think of a few that don't. These include NYP and BOS. Also, not every manned station have carts. For example, KIN is manned, but does not have a cart (or checked baggage)!
I was told by amtrak customer relations just this past monday that every manned station has assistance by a cart, the cart does not have to be for luggage, it is for assistance with mobility issues. The person I spoke with said that if there are no red caps, that asking at the ticket office, that there will be assistance to the train, either by cart with luggage area or as in EMY by a golf cart. I am just going by what I have been told. Even at WOR where I board, they have a station wheelchair if I needed that to get to the train. Believe me, I have checked for any station that I could possibly want to travel to. I cannot walk the distance of a train without ending up in extreme physical issues.