This is quite easy to do, but please understand the implications in providing access to your internal infrastructure to your customers. This can lead to security issues in the case that an unruly customer decides to be malicious on the private net.
1) Browse to the Container you wish to provide private network access to.
2) Browse to the Network Tab and Configure
3) We will now setup the Bridged Network Section:
a. Bridged Network: Select the checkbox
b. Connect to: This is not required to provide access to the SoftLayer private network.
c. Get IP Address by DHCP: Unselect this checkbox
d. IP Address / Subnet Mask: Choose an INTERNAL IP Address from your pool of private addresses.
5) At this point you will need to refresh the page from the link on the top right and you are done.