Secure inference of deep convolutional neural networks (CNNs) was recently demonstrated under RNS-CKKS. The state-of-the-art solution uses a high-order composite polynomial to approximate all ReLUs. However, it results in prohibitively high latency because bootstrapping is required to refresh zero-level ciphertext after every Conv-BN layer. To accelerate inference of CNNs over FHE and automatically design homomorphic evaluation architectures of CNNs, we propose AutoFHE: a bi-level multi-objective optimization framework to automatically adapt standard CNNs to polynomial CNNs. AutoFHE can maximize validation accuracy and minimize the number of bootstrapping operations by assigning layerwise polynomial activations and searching for the placement of bootstrapping operations. As a result, AutoFHE can generate diverse solutions spanning the trade-off front between accuracy and inference time. Experimental results of ResNets on encrypted CIFAR-10 under RNS-CKKS indicate that in comparison to the state-of-the-art solution, AutoFHE can reduce inference time (50 images on 50 threads) by up to 3,297 seconds (43%) while preserving accuracy (92.68%). AutoFHE also improves the accuracy of ResNet-32 by 0.48% while accelerating inference by 382 seconds (7%).