Normally, we Chinese have a different way of expressing this meaning, mostly a subtler way. We don't have the exactly matching expression as "i'm happy for you", as i can remember, mostly in any occasions. People usually say, "o that's good, (嗯，真不错！）” instead to show them that they feel happy for the other person.
This reminds me of another long-lasting question in my head which i cannot figure out a better translation than the literal one which seems quite not native. That is "i'm sorry to hear that" in English when you heard some bad news from another person and want to show your sympathy. Because we Chinese simply don't say this sentence in our daily dialogue. Normally we just say something good or irrelevant to try to cheer up the person.