First of all, check that you DO have another ip address on another interface at the server. Either by ifconfig or anything else.
To change the outgoing IP on a postfix mail server, edit the file /etc/postfix/master.cf
Find this part in the file,
smtp unix - - - - - smtpYou should modify it to look like below
# When relaying mail as backup MX, disable fallback_relay to avoid MX loops
relay unix - - - - - smtp
-o smtp_fallback_relay=
smtp unix - - - - - smtpOf course, change the IP address 192.168.1.1 to whatever your secondary IP is.
-o smtp_bind_address=192.168.1.1
# When relaying mail as backup MX, disable fallback_relay to avoid MX loops
relay unix - - - - - smtp
-o smtp_bind_address=192.168.1.1
-o smtp_fallback_relay=
Then restart and reload the postfix server.
[root@mail ~]# /etc/init.d/postfix restart
Shutting down postfix: [ OK ]
Starting postfix: [ OK ]
[root@mail ~]# /etc/init.d/postfix reload
Reloading postfix: [ OK ]