It seems almost taboo to discuss Beloved in the spirit of happiness. However, I would argue that there are moments of happiness in this novel, whether they are self-manufactured or based on a weak support. These moments are therefore fleeting.
Denver feels happiness when Beloved first comes to 124 because she has a companion. Her sister has finally returned to keep her company and to love her. Then, that day on the frozen pond when Beloved chokes Sethe, Denver begins to realize that her original happiness towards Beloved was possibly incorrect because she may want to hurt Sethe. When Beloved begins to take advantage of Sethe and becomes demanding of everything Sethe has, the happiness Denver feels towards Beloved is very diminished. I think to an extent, Denver still loves Beloved but she just doesn't understand why she has taken such a turn for the worse. She doesn't understand Beloved's actions yet yearns for the normalcy that she thought Beloved would bring.
Sethe too feels this immediate happiness towards Beloved and believes that Beloved will truly enrich her life. When their relationship becomes one of dependence rather than equal cooperation, Sethe feels again enslaved in the actions of another. This time though, she doesn't have the strength to overcome the chains Beloved places on her because of the immense guilt she feels about Beloved's death. Beloved allows her to feel guilty with no hope of atonement. Her happiness is again fleeting because it was based on the false notion that Beloved would be a benefit in their lives. The true moments of happiness for Sethe were the times that Paul D was there; first when he returned in the beginning and then again when she went crazy at the end and he was there again. Morrison is showing that we must be selective in the moments that we choose to be happy about.
This is the first novel in which the idea that you can create your own happiness has been challenged. Morrison creates such tragically beautiful characters that she doesn't allow for them to create their own real happiness. It's either that she doesn't let them or they are too burdened by their other worries that they cannot attempt to create happiness.