I know you don't want to gamble, but in my opinion, playing Texas Hold 'Em if the fastest way you can increase your cash, supposing you know when to stop betting and you can find someone to play in the high stake room with you.
Ball race is pretty decent. Two to three players (including you) is ideal, because everyone is guaranteed a winning bonus. Focus on getting the melons when there are only a couple of people with you (but don't bother getting more than 20 per round). It doesn't take long to play through a course, and it is a relaxing, simple game to play. A couple of hours of ball race should net you a good amount.
I enjoy playing virus too. There are 10 rounds in virus and you can get about 1500 per round if you come first (by getting most kills during the round) and survive with another player, if I am not mistaken.
If you aren't going to gamble, you should just focus on having fun in the minigames, and not focus too much on your earnings. I made about 400k in a couple of weeks of light play, mostly in minigames but also some Texas Hold 'em.