Noise and motion artifacts in Positron emission tomography (PET) scans can interfere in diagnosis and result in inaccurate interpretations. PET gating techniques effectively reduce motion blurring, but at the cost of increasing noise, as only a subset of the data is used to reconstruct the image. Deep convolutional neural networks (DCNNs) could complement gating techniques by correcting such noise. However, there is little research on the specific application of DCNNs to gated datasets, which present additional challenges that are not considered in these studies yet, such as the varying level of noise depending on the gate, and performance pitfalls due to changes in the noise properties between non-gated and gated scans. To extend the current status of artificial intelligence (AI) in gated-PET imaging, we present a post-reconstruction denoising approach based on U-Net architectures on cardiac dual-gated PET images obtained from 40 patients. To this end, we first evaluate the denoising performance of four different variants of the U-Net architecture (2D, semi-3D, 3D, Hybrid) on non-gated data to better understand the advantages of each type of model, and to shed more light on the factors to take in consideration when selecting a denoising architecture. Then, we tackle the denoising of gated-PET reconstructions, revising challenges and limitations, and propose two training approaches, which overcome the need for gated targets. Quantification results show that the proposed deep learning (DL) frameworks can successfully reduce noise levels while correctly preserving the original motionless resolution of the gates.