With that many populists, just wait until you get a non-populist consul (imprisoning populists until the only eligible consuls are non-populists works). If there is a populist majority in the senate but the consul isn't a populist, you will get a populist civil war. After winning said war, the senate will rebalance with each faction getting 20 senators.
If that doesn't work, wait until you get a fairly competent consul (or one with a competent son/s) and declare a dictatorship. Then you can play on as a monarchy without those pesky populists or you can restore the republic after a little bit. I believe that also rebalances the senate.
To prevent populists from rising up again, make sure to always have an omen up, use as many of your available trade routes as possible, have plenty of slaves and go to war from time to time. Also, check who the populist faction leader is. If he has any sort of respectable charisma (anything above 2), imprison him. The populist faction leader gives a populist attraction equal to 4 times his charisma, as compared to the other factions that only get a bonus equal to their leader's charisma. Also, don't assign any populists to any technology or government posts, as then their charisma will also increase populist attraction (but at the normal 1-to-1 rate).
That's the short answer on managing populists. For the long answer, read the quite thorough Republic Strategy Guide by Cheexsta that is stickied on this forum.