You are going to need to purchase a PS2 RF adapter. Hook the adapter into your PS2 av socket, then, using this adapter you need to connect your PS2 RF cable into the input of your cable box.
Your PS2 has an network port in the back of the system. Simply take a standard cat5 Ethernet cord and plug it into the back of either a router or the cable box.
Unfortunately, PS2s and cable boxes do not support this sort of connection. Neither device has input connections that support any sort of data, audio, or video transfer. Instead, both just have outputs that go to your speakers/receiver or TV/monitor which can't facilitate what you are trying to do.
You cannot connect a PS2 to a cable box. Maybe a Switch Board or A/V Center. PS2 my have composite cables. composite cables consist of Red, Green, Blue, and Yellow, Red, and White, RC Cable.
Match the colored jacks of the output cable of the PS2 to the same colored aux inputs of the cable box. Select the Aux source on the cable box to view the PS2.