Well, I know for a fact that after you play for a certain amount of time on the slots, sometimes a type of Pokeball may appear at the bottom screen. You can then use the pokeball as a sort of metronome to get yourself in time to press the slots at the right time.
There's also when a Clefairy appears at the bottom of your screen which is the "bonus" round. You just follow the slots that Clefairy's pointing at and you get coins straight away from that as it's always correct in where it's pointing.
I'm still not quite too sure how to make these two things happen, but when they do, they help in getting coins a lot.
Otherwise, if this is too tedious for you, the option of buying coins is always available.