https://www.amtrak.com/pets
Per the pet policy
Pets should remain entirely inside a closed carrier while in stations and onboard trains and must remain with you at all times; do not leave them alone.Onboard, place your pet carrier under your seat (not under the seat in front of you), except on Amtrak Cascades trains where you can put your pet carrier on the floor in front of the seat next to you.Pets are welcome in Coach class and Acela Business Class, but remember they may not travel in Acela First Class seating, non-Acela Business class, First Class private rooms or food service cars.Some routes designate a specific Coach car for pets: Amtrak Cascades, Carl Sandburg, Illinois Zephyr, Illini, Lincoln Service, Saluki, Pere Marquette, Wolverine, Blue Water, Hiawatha and Missouri River Runner. On other pet friendly routes, you and your pet may ride in any Coach car.
Looks like pets in sleepers are a no go. That's what I thought, but wasn't positive.