Fair-CO2 is a system for fairly attributing operational and embodied carbon in cloud data centers to user workloads. It leverages the Shapley value, a game theory solution for fair shared cost attribution with theoretical fairness guarantees. We propose the standard Shapley value solution as a ground truth for attribution in cloud data centers, addressing two key gaps in existing carbon attribution methods that lead to unfair attributions: the effect of dynamic demand on embodied carbon, and interference effects in colocated scenarios. However, the computational cost of the Shapley value solution scales exponentially with the number of workloads and becomes intractable for large systems. Fair-CO2 addresses the scalability challenges of the Shapley value while preserving its fairness benefits via two core components: demand-aware embodied carbon attribution and interference-aware resource cost attribution. Using Monte Carlo simulations of workload schedules and colocation scenarios, we show that Fair-CO2 can approximate the ground truth Shapley attribution solution at scale. We also show how users, once provided a fair way of estimating their workload carbon footprint, can dynamically optimize workload deployment for carbon savings.