Long-standing data sparsity and cold-start constitute thorny and perplexing problems for the recommendation systems. Cross-domain recommendation as a domain adaptation framework has been utilized to efficiently address these challenging issues, by exploiting information from multiple domains. In this study, an item-level relevance cross-domain recommendation task is explored, where two related domains, that is, the source and the target domain contain common items without sharing sensitive information regarding the users' behavior, and thus avoiding the leak of user privacy. In light of this scenario, two novel coupled autoencoder-based deep learning methods are proposed for cross-domain recommendation. The first method aims to simultaneously learn a pair of autoencoders in order to reveal the intrinsic representations of the items in the source and target domains, along with a coupled mapping function to model the non-linear relationships between these representations, thus transferring beneficial information from the source to the target domain. The second method is derived based on a new joint regularized optimization problem, which employs two autoencoders to generate in a deep and non-linear manner the user and item-latent factors, while at the same time a data-driven function is learnt to map the item-latent factors across domains. Extensive numerical experiments on two publicly available benchmark datasets are conducted illustrating the superior performance of our proposed methods compared to several state-of-the-art cross-domain recommendation frameworks.