The carbon footprint of data centers has recently become a critical concern. So far, most carbon-aware strategies have focused on leveraging the flexibility of scheduling decisions for batch processing by shifting the time and location of workload executions. However, such approaches cannot be applied to service-oriented cloud applications, since they have to be reachable at every point in time and often at low latencies. We propose a carbon-aware approach for operating microservices under hourly carbon budgets. By choosing the most appropriate version and horizontal scaleout for each microservice, our strategy maximizes user experience and revenue while staying within budget constraints. Experiments across various application configurations and carbon budgets demonstrate that the approach adapts properly to changing workloads and carbon intensities.