The paper presents experiments on part-of-speech and full morphological tagging of the Slavic minority language Rusyn. The proposed approach relies on transfer learning and uses only annotated resources from related Slavic languages, namely Russian, Ukrainian, Slovak, Polish, and Czech. It does not require any annotated Rusyn training data, nor parallel data or bilingual dictionaries involving Rusyn. Compared to earlier work, we improve tagging performance by using a neural network tagger and larger training data from the neighboring Slavic languages. We experiment with various data preprocessing and sampling strategies and evaluate the impact of multitask learning strategies and of pretrained word embeddings. Overall, while genre discrepancies between training and test data have a negative impact, we improve full morphological tagging by 9% absolute micro-averaged F1 as compared to previous research.