What you wrote is grammatically correct, however; I think it is more common to say "I see the happiness in your eyes" or "I can see the happiness in your eyes"

There is a saying, "eyes are the window to the soul". It means that a person can understand what is in your soul (I.e. what you are feeling) by looking into your eyes and understanding what they express. I have always thought that eyes tell so much about the person at that moment in time when you look. So, "I see happiness in your eyes" is a romantic notion. The eyes do not lie!

I would say, "You look happy" or "You seem happy". I would not say, "I see happiness in your eyes". That might seem a little weird, that you are trying to see through that person.