Graph Neural Networks (GNNs) are emerging models to analyze graph-structure data. GNN execution involves both compute-intensive and memory-intensive kernels. The latter kernels dominate execution time, because they are significantly bottlenecked by data movement between memory and processors. Processing-In-Memory (PIM) systems can alleviate this data movement bottleneck by placing simple processors near or inside to memory arrays. This work investigates the potential of PIM systems to alleviate the data movement bottleneck in GNNs, and introduces PyGim, an efficient and easy-to-use GNN library for real PIM systems. We propose intelligent parallelization techniques for memory-intensive kernels of GNNs tailored for real PIM systems, and develop an easy-to-use Python API for them. PyGim employs a cooperative GNN execution, in which the compute- and memory-intensive kernels are executed in processor-centric and memory-centric computing systems, respectively, to fully exploit the hardware capabilities. PyGim integrates a lightweight autotuner to tune the parallelization strategy of the memory-intensive kernel of GNNs and enable high programming ease. We extensively evaluate PyGim on a real-world PIM system that has 16 PIM DIMMs with 1992 PIM cores connected to a Host CPU. In GNN inference, we demonstrate that it outperforms prior state-of-the-art PIM works by on average 4.38× (up to 7.20×), and state-of-the-art PyTorch running on Host by on average 3.04× (up to 3.44×). PyGim improves energy efficiency by 2.86× (up to 3.68×) and 1.55× (up to 1.75×) over prior PIM and PyTorch Host schemes, respectively. In memory-intensive kernel of GNNs, PyGim provides 11.6× higher resource utilization in PIM system than that of PyTorch library (optimized CUDA implementation) in GPU systems. Our work provides useful recommendations for software, system and hardware designers. PyGim is publicly and freely available at https://github.com/CMU-SAFARI/PyGim facilitate the widespread use of PIM systems in GNNs.