Portuguese Sign Language (LGP) is the official language in deaf education in Portugal. Current approaches in developing a translation system between European Portuguese and LGP rely on hand-crafted rules. In this paper, we present a fully automatic corpora-driven rule-based machine translation system between European Portuguese and LGP glosses, and also two neural machine translation models. We also contribute with the LGP-5-Domain corpus, composed of five different text domains, built with the help of our rule-based system, and used to train the neural models. In addition, we provide a gold collection, annotated by LGP experts, that can be used for future evaluations. Compared with the only similar available translation system, PE2LGP, results are always improved with the new rule-based model, which competes for the highest scores with one of the neural models.