That's a really nice looking PS2 my friend/neighbor owns one just like it he works at gamestop it's smaller but don't know to much about it yet. Anyway some suggestions you can mount it under the glove comp. with custom brackets that's probably the most common place you'd want to put it. Create something that is easily accessible like puting the Inveter plug up front and AV plugs as well. I think it's just easier if you mount it in the front somewhere when changing disc. Then all you have to do is plug and play.
As for wires go buy a PS2 RF Wireless controller the type where you can play without pointing at a reciever they work great. You can also go mount it in the trunk, rear seat, etc. you can't change CD's so easily but the wireless controllers are a must have with this setup.
I've had a time when the PS2 wouldn't play CD's correctly because of the slanted position I had it mounted. I know you can mount the PS2 in a standing upright or horizontal flat position. So I don't know if mounting the PS2 in the center armrest area would be a good idea if that's what you meant but it can work you just have to mount it correctly. You may need that black plastic clip to keep the CD in the tray so it doesn't jump out of place all the time when the car is in movement it'll take away some of the CD read problems. I've went through 3 PS2's and they all have different boards different shock sensors that got messed up pretty bad. Don't know about that small PS2 one though maybe better.
If you mount it in the center console it'll be a custom job just by looking at your size comparison with the DVD. You could probably get away with it in the Armrest test how your PS2 works in that position first before doing your custom work. That would look great and it'll be easier to cut up that top lid and mold around it a bit then paint. If you wanted it inside and it fits great! No cutting needing. If it doesn't more custom work needed.
Good Luck on your mod hope all goes well. Here's a pic of my broken PS2's all dusty aha other one is in the car of couse