In recent years, there has been a notable rise in research interest regarding the integration of gender-inclusive and gender-neutral language in natural language processing models. A specific area of focus that has gained practical and academic significant interest is gender-neutral rewriting, which involves converting binary-gendered text to its gender-neutral counterpart. However, current approaches to gender-neutral rewriting for gendered languages tend to rely on large datasets, which may not be an option for languages with fewer resources, such as Portuguese. In this paper, we present a rule-based and a neural-based tool for gender-neutral rewriting for Portuguese, a heavily gendered Romance language whose morphology creates different challenges from the ones tackled by other gender-neutral rewriters. Our neural approach relies on fine-tuning large multilingual machine translation models on examples generated by the rule-based model. We evaluate both models on texts from different sources and contexts. We provide the first Portuguese dataset explicitly containing gender-neutral language and neopronouns, as well as a manually annotated golden collection of 500 sentences that allows for evaluation of future work.