Available minigames are as follows, generally you can begin and then exit out for it to count as played so long as you have spent the money to play.
Batting Cages
Black Jack
Crazy Delivery
Darts
Dondoko Island
Golf
Karaoke
Koi-Koi
Mahjong
Miss Match
Oichi-Kabu
Poker
Sega Bass Fishing
Shogi
SpikeOut
Sujimon Battle
Survival Can Collection
UFO Catcher
Virtua Fighter 3
Vocational School