The only game in the casino is a slot machine-style game. Your Itemfinder won't pick them up, though. Make sure you look around everywhere on the ground in the Game Corner: there are plenty of free coins other people have dropped, to be found as you would with any other hidden item.
Unlike more recent titles, there is no 500 coins for 10000P option: you're stuck mashing the A-button unless you decide to play a few games. At the main desk in Game Corner (in the top left corner) you can buy 50 coins for 1000P. You'll need a Coin Case, to be found in the restauraunt from the guy with the glasses along the main strip of buildings below where the Rocket Game Corner is. Here you can buy coins, test your luck, and win fabulous prizes, including new Pokemon and TMs you won't get anywhere else. The Game Corner has been a staple of every Pokemon game up to Generation IV.
