The COVID-19 pandemic has led governments worldwide to introduce various measures restricting human activity and mobility. Along with the administration of COVID-19 vaccinations and rapid testing, socio-technological solutions such as digital COVID-19 certificates have been considered as a strategy to lessen these restrictions and allow the resumption of routine activities. Using a mixed-methods approach - a survey (n=1008) and 27 semi-structured interviews - this study explores the attitudes of residents in the Republic of Ireland towards the idea of introducing digital COVID-19 certificates. We examine the topics of acceptability, fairness, security and privacy of COVID-related personal data, and practical considerations for implementation. Our study reveals the conditional and contextual nature of the acceptability of digital certificates, identifying specific factors that affect it, associated data practices, and related public concerns and expectations of such technologies.