You need to find the IP address of your PS2's network device. Configure that device to use a Static IP address and not DHCP so it doesn't change. Can't help much with that without knowing what you are using as a network connector for your PS2.
Then you need to log into your routers configuration, almost every router has a web interface that you pull up by entering your default gateway address (this is the routers IP address) into a web browser. You can find what your gateway address is on a Windows computer by going to start -> run ->type in: cmd -> hit ok. This will give you a DOS prompt. Type in the command ipconfig /all and hit enter. Right down the default gateway. Open a web browser and type that address (it's likely 192.168.1.1). It may prompt for a user name and password to enter the web interface, the default UN/PW depends on your router manufacturer(should be in the manual if you have one). Then you need to find the section of the web interface that lets you put an IP into the DMZ...and put the statically assigned IP address of your PS2's network device into it.