Monocular depth estimation is a central problem in computer vision and robot vision, aiming at obtaining the depth information of a scene from a single image. In some extreme environments such as dynamics or drastic lighting changes, monocular depth estimation methods based on conventional cameras often perform poorly. Event cameras are able to capture brightness changes asynchronously but are not able to acquire color and absolute brightness information. Thus, it is an ideal choice to make full use of the complementary advantages of event cameras and conventional cameras. However, how to effectively fuse event data and frames to improve the accuracy and robustness of monocular depth estimation remains an urgent problem. To overcome these challenges, a novel Coordinate Attention Gated Recurrent Unit (CAGRU) is proposed in this paper. Unlike the conventional ConvGRUs, our CAGRU abandons the conventional practice of using convolutional layers for all the gates and innovatively designs the coordinate attention as an attention gate and combines it with the convolutional gate. Coordinate attention explicitly models inter-channel dependencies and coordinate information in space. The coordinate attention gate in conjunction with the convolutional gate enable the network to model feature information spatially, temporally, and internally across channels. Based on this, the CAGRU can enhance the information density of the sparse events in the spatial domain in the recursive process of temporal information, thereby achieving more effective feature screening and fusion. It can effectively integrate feature information from event cameras and standard cameras, further improving the accuracy and robustness of monocular depth estimation. The experimental results show that the method proposed in this paper achieves significant performance improvements on different public datasets.