I think she's happy when she isn't anxious about things and feels like things are hanging over her head.
When David invites her to his father's wedding, "Free food, free drinks...you free?" "Me?" "Thee." Shakes maraca, smiles and says"Si." That was adorable and she seemed genuinely happy that David was inviting her, and that she could go with him.
When David takes her out on a "fine" date in "Symphony in Knocked Flat", when he arrives matching all her expectations and even surpassing some of them, she can't hold back the most beautiful smile when she sniffs the rose David gives her. It was a date, with a guy she cares about, likes to be with, and is genuinely attracted to, but she doesn't have to worry about where it's heading, or how much money he makes, whether or not he'd make a good husband and father, whether or not he can provide for her...it's just part of a bet.
When she DOES get with him, the guy she cares about, likes to be with, who she's most attracted to, she can't help but worry about where it's heading, if and how he'll provide for her and a family, etc etc.
The episodes pre-relationship, where they have fun on cases and there's sometime some casual flirtation, is when she's truly happy.
I don't think Maddie would truly be happy with David, because he won't change enough for her. You would think that since he finally gets with her at one point, and says how happy he is, that he'd buy her flowers, do really romantic stuff. Instead he just talks about bringing some toiletries to her house, and gives her some second hand plastic flowers.
But then again, she won't be truly happy with anyone that's not David either. This is the same guy that went all the way to South America just to make sure she was okay.