I've had the ps2 slim for a while now and have only recently found the need to position it up vertically and despite seeing a ps2 slim vertical stand for a few dollars plus shipping, I decided to make my own after also failing to find diy instructions on how to build one.
Step 1: Materials & Tools
BLANK CD/DVD : found in the bottom stack of a spool of cd's or dvd's
SHORT SCREW: computer case screw will fit into the hole in the bottom of the ps2 slim.
PHONE BOOK OR STACK OF NEWSPAPERS: so you can drill the cd/dvd on top of a flat surface
CORDLESS DRILL: to drill a hole into the cd for the screw using a 3.2" drill
SCREWDRIVER: to drive the screw into the ps2 slim's pre-existing hole
Step 2: MAKING IT!
Place the cd/dvd on top of your phonebook/newspaper base. Drill a whole in the cd anywhere on the inside ring furthest away from the center hole and make sure the screw fits. Turn the ps2 slim upside down and using a screwdriver, screw in the cd/dvd stand base you just made. Turn it back around and Voila you're done. If you want or need it sturdier you can glue several of these blank cd/dvd's together drill the hole and use a longer screw. It worked for me as I just needed it to stand up vertically.