Convolutional neural networks (CNNs) are widely applied in real-time applications on resource-constrained devices. To accelerate CNN inference, prior works proposed to distribute the inference workload across multiple devices. However, they did not address stragglers and device failures in distributed inference, which is challenging due to the devices' time-varying and possibly unknown computation/communication capacities. To address this, we propose a distributed coded inference system, called CoCoI. It splits the convolutional layers of CNN, considering the data dependency of high-dimensional inputs and outputs, and then adapts coding schemes to generate task redundancy. With CoCoI, the inference results can be determined once a subset of devices complete their subtasks, improving robustness against stragglers and failures. To theoretically analyze the tradeoff between redundancy and subtask workload, we formulate an optimal splitting problem to minimize the expected inference latency. Despite its non-convexity, we determine an approximate strategy with minor errors, and prove that CoCoI outperforms uncoded benchmarks. For performance evaluation, we build a testbed with Raspberry Pi 4Bs. The experimental results show that the approximate strategy closely matches the optimal solution. When compared with uncoded benchmarks, CoCoI reduces inference latency by up to 34.2% in the presence of stragglers and device failures.