Well, not a show, but there’s a Russian book series - and several movies based on it - about Erast Fandorin, a 19th-century detective. He stutters, and what’s special about this series is that it’s not focused on his stutter in any way. He isn’t trying to overcome it or struggling with it like in The King’s Speech, and he isn’t mocked for it either. It’s just one of his traits. All other stuttering characters I’ve seen are defined entirely by their stutter.