We present a custom implementation of a 2D Convolutional Neural Network (CNN) as a viable application for real-time data selection in high-resolution and high-rate particle imaging detectors, making use of hardware acceleration in high-end Field Programmable Gate Arrays (FPGAs). To meet FPGA resource constraints, a two-layer CNN is optimized for accuracy and latency with KerasTuner, and network quantization is further used to minimize the computing resource utilization of the network. We use "High Level Synthesis for Machine Learning" (hls4ml) tools to test CNN deployment on a Xilinx UltraScale+ FPGA, which is a proposed FPGA technology for the front-end readout system of the future Deep Underground Neutrino Experiment (DUNE) far detector. We evaluate network accuracy and estimate latency and hardware resource usage, and comment on the feasibility of applying CNNs for real-time data selection within the proposed DUNE data acquisition system.