Africa has over 2000 indigenous languages but they are under-represented in NLP research due to lack of datasets. In recent years, there have been progress in developing labeled corpora for African languages. However, they are often available in a single domain and may not generalize to other domains. In this paper, we focus on the task of sentiment classification for cross domain adaptation. We create a new dataset, NollySenti - based on the Nollywood movie reviews for five languages widely spoken in Nigeria (English, Hausa, Igbo, Nigerian-Pidgin, and Yoruba. We provide an extensive empirical evaluation using classical machine learning methods and pre-trained language models. Leveraging transfer learning, we compare the performance of cross-domain adaptation from Twitter domain, and cross-lingual adaptation from English language. Our evaluation shows that transfer from English in the same target domain leads to more than 5% improvement in accuracy compared to transfer from Twitter in the same language. To further mitigate the domain difference, we leverage machine translation (MT) from English to other Nigerian languages, which leads to a further improvement of 7% over cross-lingual evaluation. While MT to low-resource languages are often of low quality, through human evaluation, we show that most of the translated sentences preserve the sentiment of the original English reviews.