You can use any TV (no need for it to be a smart TV) as a monitor for a PC or laptop, if it has hdmi. See if you can run the program that runs shows the schedule on any PC, server or laptop that has hdmi and (preferably) can be connected to two monitors at the same time (one for you, and one for the "projector".

An alternative would be a TV that's smart enough to run a browser, and have a website with the rotating schedule. But even then, a simple mini-PC or Android box to run the browser and use the TV as a monitor would probably be a better solution then a smart TV.

You can't program the TV, so you must program something else.