You don't plug your PS2 into the FIOS box. That won't work.
What you need to do is go buy a switch box that can output RF video. These are sold at any store that sells TV accessories. They're usually advertised as "Connect your DVD player to any TV!" type of thing.
Anyways, the switch has a RF input, a RF output, and 3 or 4 additional inputs for devices using the standard AV cable (the yellow, red and white ones)
At home, you'll disconnect the FIOS box from your TV, and connect it to the RF input port on the switch. Now take a separate RF cable (usually included, or just buy a cheap one from the store) from the switch's RF output port to your TV. You should still be able to watch TV as normal with this setup.
Now connect the PS2 to one of the inputs on the switch. Let's say, #1.
Turn on the PS2, and hit the #1 button on the switch and you should see the PS2 on your TV. Hit the RF button, and you should see the channel from your FIOS box.
This way, you can connect other devices up in the future by just connecting them to the switch. This includes things like a DVD player, or even your FIOS box if you wanted. Then just hit the proper button on the switch for that device.