In standard Mandarin, "幸福" has two meaning.
1. n. happiness
2. adj. happy
So, "你的幸福" is right, but "你的幸福着" is wrong.
However, "幸福" is also an adjective, so in a sentence we can consider it as a verb and we can say "他幸福着呢。" （He's really happy now.）
Here "着" is a suffix, usually added after a verb, indicating "something is happening or in a continuous statement".
门开着。The door is open.
他吃着饭呢。He is eating meal.
Anyway, this "着" is quite complicate in Chinese, hope my answer will be helpful, and if you have more question, you are mostly welcome to contact with me. : )