Animation textures is something I'm still inexperienced in but, based on what I know, I think you could use the first approach from my response to Dascu (below).
Here're two methods I thought up with my limited knowledge in texture animation (so they are probably not the optimal solutions):
Option 1: Texture altas
Start with a large texture (however, I believe Unity won't load anything larger than 4096x4096 pixels), map the object's UV coordinates to a small fraction of that texture (say, a 64x64 "tile"), and then move the texture's offset within Unity so that it jumps from one tile to the next. For example, if the texture consists of 2x2 tiles, the UV offset for each of them would be:
Tile #1: 0,0
#2: 0, 0.5
#3:0.5, 0
#4: 0.5, 0.5
That means you'd render four frames of animation and place them in a 2x2 pattern inside the texture atlas. It's probably the easiest thing to do, but you'll have to limit frame sizes to make sure they all fit inside a texture, and you should try to keep texture sizes low if you're aiming for compatibility. Individual frames don't have to be square (you could have a 7x3 grid if you wanted), but you should keep the whole texture's size as powers of two to prevent Unity from wrecking the image by automatically stretching or reducing it to a Po2 size.
Option 2: Render to texture
I think this is a Unity Pro only feature, but if you have it or intend to purchase it for your game, you should look into it. I don't know much about it since I've never used Unity Pro myself, but I think it uses a on-scene camera to capture an image and save it to a texture you can assign to your TV. This method should result in smoother animations, but it'll probably be more expensive (since Unity will need to continously render the camera's input) and forces you to rely on in-game real-time animations, so you'll have to take the rendering budget into account.
I'm not sure if there's some kind of video-to-texture support or something along those lines, but I guess you could look into it.
Can you not just change the material's texture frame by frame? I'd guess using a small texture would be better than using a small portion of a massive texture.
So just set up a script with a list of textures, set the update rate, and point it at the target material...?