Under the dependencies section, put
<crate name>={git="ssh://git@github.com/<organization>/<reponame>.git"}
It is pretty similar to a github repo's ssh cloning link, however the : is replaced with a / and ssh:// is prepended to the URL.
git@github.com:my-organization/my-repo.git vs ssh://git@github.com/my-organization/my-repo.git
The SSH URL needs to be used because Cargo is currently unable to handle the authentication prompt that comes up when an HTTPS link is used.
Make sure that the matches the crate name in the target repo's Cargo.toml. The repo name will not override what is in the Cargo.toml if it is a different value.