It is essential to monitor marine wildlife to build effective marine mammal management plans for the development of open ocean aquaculture (OOA) around New Zealand (NZ). However, this task is challenging due to the complexities of marine ecosystems, vocal plasticity and diversity of marine mammals, and the limitations of current models. In this paper, we design methods for automatic bottlenose dolphin click detection from easily available acoustic data, which is the initial step towards building an intelligent marine monitoring system in NZ. We collect a vast amount of acoustic data from NZ waters through the use of passive acoustic monitoring and design a preprocessing strategy that converts raw audio signals into spectrograms. A dataset of bottlenose dolphin click detection is created. Four traditional image classification methods and six convolutional neural networks (CNNs), i.e., LeNet, LeNet variants, and ResNet-18, are designed to solve this task. The results show that ResNet-18 achieves the best accuracy (97.44%) among all the methods on this task. This work represents the first study using CNNs for detecting dolphin echolocation clicks.