Log in as crichtonj, or use su crichtonj to act as that user temporarily. First, set up the SSH keys for this user:
You can accept all the defaults, and do not specify a passphrase. Just press ENTER when asked to enter a passphrase. Otherwise, you cannot automate the back up process.
Next, you need to send the public key to the server to be backed up, and append it to the end of a file called authorized_keys.
You can now test to see if you can log in as oneilj on the server to be backed up without being asked a password:
If this does not ask you for a password, and lists the content of the home folder of oneilj, then the configuration is successful.