The next time your player gets sent off, either give him an official warning or fine him some wages. This will increase your Discipline rating as a manager and should, hopefully, prevent your players from picking up too many cards.
Also, check what is the tackling mentality of your Assistant Manager. Sometimes, the Assistant Manager always likes to tackle hard. So, if you leave him in charge of games, or if you apply Assistant's Advice for Opponent Instructions, you may find that a lot of opponents have been set to "Hard Tackling", which could result in more cards.
Also, if you're really desperate, then set your tackling mentality (Team Instructions>>Advanced) to "More cautiously".
And finally, try to find if there are any regular culprits, i.e. if there are 2-3 players who pick up most cards. Go into Player Instructions >> Advanced, and set tackling to "Easy" or "More cautious" or whatever it says.
All the best, let me know if these worked for you!