The tremendous growth of social media users interacting in online conversations has led to significant growth in hate speech, affecting people from various demographics. Most of the prior works focus on detecting explicit hate speech, which is overt and leverages hateful phrases, with very little work focusing on detecting hate speech that is implicit or denotes hatred through indirect or coded language. In this paper, we present CoSyn, a context-synergized neural network that explicitly incorporates user- and conversational context for detecting implicit hate speech in online conversations. CoSyn introduces novel ways to encode these external contexts and employs a novel context interaction mechanism that clearly captures the interplay between them, making independent assessments of the amounts of information to be retrieved from these noisy contexts. Additionally, it carries out all these operations in the hyperbolic space to account for the scale-free dynamics of social media. We demonstrate the effectiveness of CoSyn on 6 hate speech datasets and show that CoSyn outperforms all our baselines in detecting implicit hate speech with absolute improvements in the range of 1.24% - 57.8%.