hmm...well if you think about the themes than you can probably get the main conflicts in the novel. Think about the themes that are discussed in the enotes section. THose are Order and Disorder, Death and Resurrection, and Memory and Reminisence.
Thinking about Order and Disorder, clearly the first conflict to come to mind would be the order and disorder in Revolutionary France, the setting that Dickens has chosen for the novel. That conflict (between the revolutionaries and the nobility) is the center conflict of the whole novel.
Within the theme Death and Resurrection there are many conficts that you could discuss. Dr. Manette, who has been held in prison for almost twenty years was resurrected with a new life, and the conflict that wages within himself is another central conflict of the novel. Manette cannot quite shake the hold his burial and rebirth has on his mind. He reverts to his cobbling—a sign of his madness contracted in prison—during periods of stress.
Finally, within memory and Reminiscence think about how these conflicts lead the plot. FOr example Madame Defarge's hatred of aristocrats in general and St. Evremonde in particular is based on her memory of the rape and deaths of her siblings at his hands. She cannot forget this, and her thirst for revenge and conflict pulls along the plot.