Your best bet would be to buy a router from your local big box electronic store and set up a simple home network. This way you can have the protection of the NAT firewall (in the router) and your Mac does not have to be on to use the internet of the PS2. When you set the router up (READ THE ROUTER'S MANUAL) just open the ports the PS2 in a DMZ port forwarding to the PS2 ONLY (not the Mac).
Mac Pro Dual 2.8 Quad (2nd gen), 14G Ram, Two DVD-RW Drives, OS X 10.8.3
2006 Mac Book Pro 2.16 (first Gen) OS X 10.7.4
2TB Time Capsule, 2 TB
32G iPhone 4S Black, iPad (3rd Gen) 32G Black