tldr: Night trains make sense on routes 9-14 hours long and we can design a 50 berth single level sleeper car.
One of the key factors that influences Amtrak service is what is often called the 750 mile rule, that is routes over 750 miles are long distance and Federally funded, routes under 750 miles are corridors and at least partially state funded. Now part of the problem that this causes is that there are many routes in the that would be very successful as both night train and day trains like the Palmetto, but may not be funded by the states etc.
This post seeks to examine how efficient (and possibly profitable) services could be run on twice daily routes that are 9 to 14 hours long.
9 hours is close to the shortest you can get a decent sleep on a night train from one end to the other. 14 hours is close to the longest that most night trains in Europe or elsewhere run. But we also don't want to have night trains only that sit around all day and don't get used, it would be a waste of capital funds. So we should try to turn them around and use them for a daylight run in the opposite direction. If we could be very efficient at refuelling, cleaning and restocking the train we might be able to do it in an hour, add another hour or two to allow for some late running and we could have the train complete its run, and ready to go in the other direction in either 12 hours (just two train sets for twice daily operation) to 18 hours (three train sets for twice daily operation).
Night trains generally attract 10-25% of the air travel market on a given route, most European routes fall in the 15% mark. If you can think of an airmarket between two cities 9-14 hours apart by rail with an air travel market of >1 million passengers a year it is likely a winner - others might not have enough supply or air routes but have busy interstates instead.
Routes like this are:
San Francisco to Los Angeles (potentially extended to be Sacramento to San Diego)
NYC to Toronto
Portland, OR to Vancouver, BC
Salt Lake City to Denver via Ogden and Cheyenne
Detroit to DC via Cleveland and Pittsburgh - likely far more convenient for people in Toledo and Cleveland, slightly shorter as well.
Routes that would be if upgraded for slightly higher average speeds (approx. 60 mph)
Extra Atlanta to DC or NYC trains would be useful beyond the once a day Crescent. For instance reviving the Silver Comet as part of the SEHSR works from Raleigh to Richmond to DC might allow a 15 hour schedule to NYC.
Topeka/Kansas to Cincinnati via St Louis and Indianapolis
Chicago to Atlanta
Dallas-Forth Worth to Nashville via Little Rock and Memphis
The trains you might want; Viewliner III
A quick sketch of a possible Viewliner III 
The above diagram show the kind of 10-car train you might want to run. Cars are a standard 85 ft long by 10' 6" wide by 14 ft tall.
Sleeper types:
P - Premium, similar to current bedroom 7ft by 8ft, includes double bed, plus two single bunk beds, bathroom and a couch plus chair in the day configuration
C - Couchette or perhaps Coach Sleeper; 7ft by 6ft 10" Compartments with either 6 bunk beds or 6 seats, shared bathrooms, curtains for privacy for each bunk. (Since they are shared they would likely be segregated by gender).
S - Solo Suite, like capsule hotels or mini cabin on OBB NightJet. Single person rooms with shared bathrooms
A - Accessible, accessible 3-adult bedrooms with ensuite accessible bathroom.
Seats can be used as both first class day travel and sleeping cars at night helps generate more revenue. Coffee station and washrooms are in each sleeping car, bigger luggages items must be checked through in the baggage compartment. Extra showers and toilets are in the crew/baggage car rather than in the sleeping cars which would help have high capacity sleepers.
Twin-set Dining/First class lounge joined with galley/cafe car, would provide food service on board. The Dining car could have a similar set up to the Cross Country Cafe cars plus a proper bar and perhaps piano for live music (alcohol service is profitable on trains - even if food might not be). One big combined galley would serve both meaning that the Cafe could have meals better than just a microwaved one, maybe simple meals like fresh curry, soup etc.
Sleepers are primarily marketed towards business travellers who may want to skip the hassle of flying on at least one leg and skip a extra hotel night by taking a hotel on wheels, as well as anyone looking for a budget way to travel. With the couchette providing sleeping accommodations on a budget - maybe 50% more than coach fares?
Good food service on-board in a dining car, a comfortable lounge, and a private space to work and with free wi fi might help attract more premium passengers during the day time legs of the train.
Plentiful numbers of 2+2 coach seats with seat pitch of about 40" (approximately in-between the current long distance seat pitch and short distance Amfleet seat pitch) equivalent to Premium Economy on an airliner.
During the day leg, they would capture a wide variety of travel as may Amtrak corridor trains do while running through the day. During the night these trains provide rooms more extravagant and spacious than the current bedrooms do, as well as Solo Suites suitable for business travellers and couchette accommodations for those on a budget.
These kinds of trains and services would really help boost Amtrak's perception as a useful and good way to travel in the public's mind, and might even be new routes that aren't all that money losing after all.