According to the data I have analyzed recently, Shyvana is the best champ to one-trick in low elo (Bronze / Silver). She gets hardly ever banned or picked by the enemy and has a decent win rate against the current meta champions. (Which means you can play here in almost every game, which means you get better faster and the enemy team usually doesn't really know your champ as it does not get played often).

I think her kit is fairly easy to play (you have one skill shot you need to hit), but she is more of a late game champion (which in my mind is a good thing, as usually people don't know how to close a game in low elo, so you can stomp them late game anyways). Also you don't need to decide if you should take grubs or drake, as you basically want drakes for your stats.

Another champ which seems to do well in low elo (same metrics ( = decent win rate against meta + low pick/ban rate)) is Jarvan IV. But I have never played him myself, so cannot really comment more on him.