keep in mind that if you are pulling an IP via dhcp, you would have to out wait the lease time for a renewal (stop/start or restart) to give you a new IP.
if you are pulling an IP directly from your ISP, then you would have to call them to find out what the DHCP lease time is. their level 1 techs will not even have a clue as to what that is so you will have to get bumped up to level 2 techs to get that kind of information. not to mention in most ISPs level 2 should also have the ability to force an IP roll on you.
if you are pulling an IP from your router, then just go in and adjust the dhcp lease time. default for most routers is something around 24-48hrs. set it to 1min, then you can bring down your eth0 wait a min or 2, then bring it back up and you should then be able to pull a new IP.