Keating did not care so long as his clients were impressed, the clients did not care so long as their guests were impressed, and the guests did not care anyway. (1.6.32)
Rand is hammering home the idea that happiness based on impressing others is futile—everyone here is trying to ultimately impress a group of totally clueless guests.
"May God bless you - or whoever it is that is alone to see the best, the highest possible to human hearts. You're on your way into hell, Howard." (1.11.14)
Cameron's warning here may not seem like it ties into the book's happiness theme, but this book takes happiness to mean a sort of passion that you can't live without, not merely feeling cheerful. Roark here is setting off to pursue his passion, even though it will be hard.
"You call that freedom?" "To ask for nothing, To expect nothing. To depend on nothing." "What if you found something you wanted?" "I won't find it. I won't choose to see it." (1.12.79-82)
Dominique contradicts herself here, as usual. She longs for freedom, which she takes to mean being free, literally, from everything. But she also refuses deliberately to see things she might want. As a result, she isn't free at all.
"Will you be happy if you seal yourself for the rest of your life in that borrowed shape? Or if you strike free, for once, and build a new house, your own?" (1.13.84)
Roark tries to counsel his poor clients with philosophy. This client just wants a nice Southern mansion, but instead he gets a lecture. One man's "borrowed shape" is another man's dream house, Roark.
Dominique had spent so many summers and winters, surrounding herself with people in order to feel alone, that the experiment of actual solitude was an enchantment to her and a betrayal into a weakness she had never allowed herself: the weakness of enjoying it. (2.1.14)
Once again, Dominique seems to be unwittingly participating in Toohey's world view by viewing enjoyment as a sort of weakness. The diction here is worth noting, too. The word "enchantment" gives us the sense of a fairy tale, underlining the fact that Toohey's worldview is as far from reality as the story of Cinderella.
His normal assurance in meeting people had vanished; but he felt at ease, as if all responsibility were taken away from him and he did not have to worry about saying the right things. (2.3.52)
Happiness for Keating seems to be a lack of pressure and worry. He's so scared of responsibility that he can't be happy with it.
They were simply four people who liked being there together. (2.11.265)
This quiet scene of Mallory, Roark, Dominique, and Mike hanging out at the Stoddard Temple is one of the nicest scenes in the entire book. They're just being pals.
"I've never met the men whose work I love. The work means too much to me. I don't want the men to spoil it." (4.2.45)
The idea of men spoiling things they create is definitely foreign to Roark and his crowd, who basically are what they create. And the union between who they are and what they do is what makes them happy.
"Every form of happiness is private." (4.11.64)
Roark's idea of happiness as private becomes very political when put in opposition to Toohey's view on happiness as a sort of public commodity that should be shared and not experienced by one individual.
"We've tied happiness to guilt. And we've got mankind by the throat." (4.14.91)
Toohey's secret to success is revealed here, though he didn't originate this idea. He implies he hopped on board a bandwagon of religious and political teachings that date back a pretty long time—those Puritans weren't overly cheerful, after all.
She thought, I've learned to bear anything except happiness. I must learn how to carry it. (4.17.14)
Leave it to Dominique to turn happiness into some sort of burden that she has to figure out how to manage. Good grief.