Understanding the public sentiment and perception in a healthcare crisis is essential for developing appropriate crisis management techniques. While some studies have used Twitter data for predictive modelling during COVID-19, fine-grained sentiment analysis of the opinion of people on social media during this pandemic has not yet been done. In this study, we perform an in-depth, fine-grained sentiment analysis of tweets in COVID-19. For this purpose, we perform supervised training of four transformer language models on the downstream task of multi-label classification of tweets into seven tone classes: [confident, anger, fear, joy, sadness, analytical, tentative]. We achieve a LRAP (Label Ranking Average Precision) score of 0.9267 through RoBERTa. This trained transformer model is able to correctly predict, with high accuracy, the tone of a tweet. We then leverage this model for predicting tones for 200,000 tweets on COVID-19. We then perform a country-wise analysis of the tone of tweets, and extract useful indicators of the psychological condition about the people in this pandemic.