The fair top-k node ranking problem aims to find the k most significant nodes in a network without discriminating against particular groups of nodes as defined by their protected attribute. However, unlike fair ranking problems for independent and identically distributed (i.i.d.) data, the rank assigned to a node may influence the perception of fairness among its neighbors with similar acceptability scores due to the interconnectivity among the nodes. Fairness perception, which is an individual-level fairness metric, has thus been proposed to measure the degree to which a node perceives its ranking outcome as fair. While existing fair node ranking algorithms can help maximize its fairness perception, they are susceptible to the oversmoothing effect due to their message passing mechanism. Thus, a key challenge in designing fair node ranking algorithms is to balance the trade-off between maximizing the acceptability of the highly ranked nodes while satisfying both individual-level and group-level fairness criteria. To address this challenge, this paper presents a novel framework called DeepFairRank that integrates the potentially diverging criteria in a unified, multi-objective optimization framework using neural networks. Experimental results demonstrate the effectiveness of the framework when applied to real-world data.