Confidential virtual machines (CVMs) are designed to protect data in cloud machines, but they fail in this task in common Software-as-a-Service (SaaS) cloud environments. In such settings, the software stack within a CVM, including service programs and the operating system, that receives and processes data may intentionally disclose it to attackers. We present Erebor, a sandboxing architecture for CVMs that processes client data in secure containers, where restrictions apply to both (a) access by all untrusted outside components and (b) the sandbox's ability to communicate data through memory and software-controlled direct or covert exits. Erebor enables such restrictions through a security monitor design based on intra-kernel privilege isolation for CVM, fully compatible with emerging cloud deployments without requiring host modifications. Under realistic scenarios, such as large language model inference and private information retrieval, Erebor only adds a performance overhead of 4.5%-13.2%, demonstrating its practicality in terms of enabling strong data sandboxing in modern cloud machines.