Multilingual transformer models like mBERT and XLM-RoBERTa have obtained great improvements for many NLP tasks on a variety of languages. However, recent works also showed that results from high-resource languages could not be easily transferred to realistic, low-resource scenarios. In this work, we study trends in performance for different amounts of available resources for the three African languages Hausa, isiXhosa and Yorùbá on both NER and topic classification. We show that in combination with transfer learning or distant supervision, these models can achieve with as little as 10 or 100 labeled sentences the same performance as baselines with much more supervised training data. However, we also find settings where this does not hold. Our discussions and additional experiments on assumptions such as time and hardware restrictions highlight challenges and opportunities in low-resource learning.