Currently there's no out-of-the-box support for private registries, but we have definitely designed room for it in Cargo!
The plan in Cargo is to support adding custom registries to a Cargo.toml, with the default being the current crates.io registry. Dependencies are then tagged which registry they come from so you can have crates from a private registry. Note that this feature is intended to be orthogonal to mirrors.
The main sticking point I haven't had time to think through is cross-registry dependencies. Presumably crates in a private registry need to depend on those from crates.io, yet I'm not entirely certain how to do this.