Studies investigating the COVID-19 pandemic from a psychological point of view have mostly focused on psychological distress. This study adopts the framework of existential positive psychology, a second wave of positive psychology that emphasizes the importance of effective coping with the negative aspects of living in order to achieve greater wellbeing. Trait emotional intelligence (trait EI) can be crucial in this context as it refers to emotion-related personality dispositions concerning the understanding and regulation of one’s emotions and those of others. The present study investigated the relationship between trait EI and both wellbeing and psychological distress (i.e., depression, anxiety, and stress), while exploring the mediating role of meaning-centered coping (proactive transformative strategies based on meaning in life) and maladaptive coping (i.e., behavioral disengagement and self-blame) during the first few months of the COVID-19 pandemic. A sample of 326 Lebanese adults completed measures of trait EI, wellbeing, psychological distress, coping, and meaning-centered coping. Results showed a strong positive correlation between trait EI and meaning-centered coping. Trait EI also correlated positively with wellbeing and negatively with psychological distress. Structural equation modeling showed that meaning-centered coping partially mediated the relationship between trait EI and wellbeing. Maladaptive coping fully mediated the relationship between trait EI and psychological distress. Findings indicate that trait EI is positively related to dealing with a stressful situation such as the pandemic in positive ways at both the cognitive level, by reformulating the situation to see something valuable in it, and behavioral level, by being proactive about it. Trait EI was positively linked to seeing the situation as an opportunity for personal growth, finding personal meaning in this situation, maintaining an attitude of hope and courage, and acting more responsibly with one’s self and others during the current crisis. In turn, this coping formula was related to lower psychological distress and improved mental health. These results are consistent with the existential positive psychology framework and can inform implementation programs and policies aiming at raising awareness and promoting healthy and successful coping during the pandemic.