To show that money doesn't buy happiness, you do not need to look much further than the first chapter that depicts Nick's visit to the Buchanan house. Here there is everything that money can buy: polo horses, a Georgian mansion, a life of leisure. Yet, Daisy is unhappy that her husband is having an affair. Tom himself hardly seems happy. He has a "hard mouth and a supercilious manner" and his gruff voice adds to the "impression of fractiousness he conveyed." Nick goes on to add
there were men at New Haven who had hated his guts.
Inside the gorgeous Buchanan mansion, Daisy and Jordan are listless and bored. They wonder what people plan. Since they themselves have no plans and entertain themselves with inane small talk, their lives seem sterile and stagnant. Daisy's first words are
"I'm p-paralyzed with happiness."
Indeed she is paralyzed, trapped in a golden cage, but not with happiness, but with her wealth.
If you go further, in Chapter 8, after Daisy has returned home to Tom after the hit and run accident, Gatsby is sitting alone in his large, cold mansion. Nick describes it in negative terms:
His house had never seemed so enormous to me as it did that night when we hunted through the great rooms for cigarettes. We pushed aside curtains that were like pavilions and felt over innumerable feet of dark wall for electric light switches--once I tumbled with a sort of splash upon the keys of a ghostly piano. There was an inexplicable amount of dust everywhere and the rooms were musty . . .
Gatsby's dark, dusty house represents his emptiness now that his dream of turning back time and starting anew with Daisy has died. For all their money, Gatsby nor Daisy nor Tom seems particularly happy. They are all seem empty, directionless, and stagnant.
To support the idea with quotations from the novel, you will need to provide some context, I think. For instance, in Chapter VII Myrtle Wilson is killed on the road. Gatsby drives Daisy home, but he does not leave. He stands outside on the lawn, watching over Daisy, who is inside having a quiet supper with her husband. When Nick encounters him, Gatsby says he will stay all night if necessary to "protect" Daisy. Nick sees Tom and Daisy through a window and observes that they are sitting close together, no conflict between them. At the end of the chapter, Nick says this of Gatsby:
He put his hands in his coat pockets and turned back eagerly to his scrutiny of the house, as though my presence marred the sacredness of the vigil. So I walked away and left him standing there in the moonlight--watching over nothing.
The passage makes it clear that all of Gatsby's wealth will not give him the one thing he wants most: Daisy. She remains with Tom, by choice, while Gatsby stands outside alone in the dark. His money will not buy his way into her life.
A passage in the conclusion of the novel is also significant in supporting the idea that money will not buy happiness:
He [Gatsby] had come a long way to this blue lawn and his dream must have seemed so close that he could hardly fail to grasp it. He did not know that it was already behind him, somewhere back in that vast obscurity beyond the city, where the dark fields of the republic rolled on under the night.
Gatsby had indeed come a long way, raising himself out of poverty as a boy growing up in North Dakota. He had built a great fortune, bought a huge mansion, and acquired every material possession he desired. However, his money did not fulfill his dream. He did not find happiness because Daisy remained beyond his reach. His dream was "behind him," back in North Dakota; no amount of money would change the circumstances of his birth; no amount of money would make him acceptable in Daisy's upper class world of inherited wealth. He had come "a long way," but happiness remained just out of his reach. Again, he could not buy what he most wanted; he could not buy his dream.