Cloud computing has become the de facto paradigm for delivering software to system users, with organizations and enterprises of all sizes making use of cloud services in some way. On the surface, adopting the cloud appears to be a very efficient approach for offloading concerns such as infrastructure management, logistics, and most importantly for this work, energy consumption and consequent carbon emissions to the cloud service provider. However, this is in many ways not an appropriately accountable solution to managing the contribution of the ICT sector to global emissions. To this effect, in this paper we report on an exploratory case study done in collaboration with a Software as a Service provider operating globally in the telecommunications sector. The study reckons with the service provider using multi-tenant, that is, shared, off-premises data centers for hosting their private cloud infrastructure towards developing a fair model of allocating operational emissions among the service tenants -- customer companies with many distinct users. The developed emissions model has to account for allocating in an appropriate manner the generated emissions between the tenants of the software provider services, and among the different tenants of the same data center. A carbon footprint report generator is developed building on the proposed model which is, in turn, used to present sustainability reports to involved stakeholders for evaluation purposes. Our results show that the model is perceived as transparent, informative, and fair, with requested improvements focusing mainly on the generated reports and the information contained therein.