High-quality, multi-channel neural recording is indispensable for neuroscience research and clinical applications. Large-scale brain recordings often produce vast amounts of data that must be wirelessly transmitted for subsequent offline analysis and decoding, especially in brain-computer interfaces (BCIs) utilizing high-density intracortical recordings with hundreds or thousands of electrodes. However, transmitting raw neural data presents significant challenges due to limited communication bandwidth and resultant excessive heating. To address this challenge, we propose a neural signal compression scheme utilizing Convolutional Autoencoders (CAEs), which achieves a compression ratio of up to 150 for compressing local field potentials (LFPs). The CAE encoder section is implemented on RAMAN, an energy-efficient tinyML accelerator designed for edge computing. RAMAN leverages sparsity in activation and weights through zero skipping, gating, and weight compression techniques. Additionally, we employ hardware-software co-optimization by pruning the CAE encoder model parameters using a hardware-aware balanced stochastic pruning strategy, resolving workload imbalance issues and eliminating indexing overhead to reduce parameter storage requirements by up to 32.4%. Post layout simulation shows that the RAMAN encoder can be implemented in a TSMC 65-nm CMOS process, occupying a core area of 0.0187 mm2 per channel. Operating at a clock frequency of 2 MHz and a supply voltage of 1.2 V, the estimated power consumption is 15.1 uW per channel for the proposed DS-CAE1 model. For functional validation, the RAMAN encoder was also deployed on an Efinix Ti60 FPGA, utilizing 37.3k LUTs and 8.6k flip-flops. The compressed neural data from RAMAN is reconstructed offline with SNDR of 22.6 dB and 27.4 dB, along with R2 scores of 0.81 and 0.94, respectively, evaluated on two monkey neural recordings.