The easiest/fastest way to earn Tokens in the Casino is Kopin Racing. You should always bet the max of 500 tokens, as race difficulty is determined by the Kopins racing and not how much you wager. Each Kopin has their own walk speed, run speed, boost stamina, boost recharge, etc.
Woody is probably the fastest and easiest to win with. Unfortunately, his payouts are usually between 2.0x and 3.0x, sometimes they go up above 5.0 in which case you should definitely use him.
Nanmy has the highest multiplier of the Kopins you can easily win with, usually between 5.0 and 7.0. Note that if Nanmy and Woody are up against eachother it's very hard to beat Woody with Nanmy, but his payout is high enough that you want to use him against other Kopins.
Joshua is also great, his payouts range from 3.0 to the mid 5.0s. I've beaten Nanmy/Woody with him a bunch of times, he's usually my go-to guy especially when his payout gets over 4.0.
How to actually race: pay attention to your Kopin, they have a slow trot and a fast run, you can tell the difference by the way the lean forward slightly when they run and it's (obviously) faster. While they're running shake the wiimote (tap a on the classic controller) to make them go faster, you won't get much of a speed boost from it if they're just walking. Make sure you stop before your stamina bar is completely empty, otherwise they'll overheat and stop dead in the middle of the track.
Using the above method you can easily make ~3000 tokens every 1-2 minutes.