Morphologically rich languages often lack the annotated linguistic resources required to develop accurate natural language processing tools. We propose models suitable for training morphological taggers with rich tagsets for low-resource languages without using direct supervision. Our approach extends existing approaches of projecting part-of-speech tags across languages, using bitext to infer constraints on the possible tags for a given word type or token. We propose a tagging model using Wsabie, a discriminative embedding-based model with rank-based learning. In our evaluation on 11 languages, on average this model performs on par with a baseline weakly-supervised HMM, while being more scalable. Multilingual experiments show that the method performs best when projecting between related language pairs. Despite the inherently lossy projection, we show that the morphological tags predicted by our models improve the downstream performance of a parser by +0.6 LAS on average.