I don't know about other people's methodology when dealing with populists, but I have a few golden rules when dealing with the likes of them
1) Most importantly, look who your next consul is likely to be. If one of them is a populist, smear his reputation, which should effectively rig the election against him. if this fails send him of with an army you don't like/ is crap, and have him lose a load of battles against barbarians, deep in the wilderness... :rofl:
2) Never, ever let a populist get a position of power (navy, army, governovership, admin post, censor, etc.) if they get prominence and popularity, neither of which is good (for a populist to have

) then you are in deep doodoo, and you could end up with a populist consul
3) Watch their political attraction! That golden information is the first clue you get to knowing if they are about to landslide the senate in their favour... I've seen a Populist Leader who got his faction 20% political attraction alone :wacko: which is insane. He didn't even have any titles or anything, sheer charisma. If such an individual appears for the populists in your game, then imprison him. you may be unlucky and have to imprison a bunch in a row, but with the frequent Consul change, the tyranny hit will be cut down pretty quick (it halves with every new leader, and goes down monthly anyways)

Leave low charisma (less than four) populist leaders in control of their faction. Also watch out for inactive trade-routes, and other problems that increase their political attraction; these can be easily fixed with a little attentiveness. War exhaustion and long periods of peace also increase their political attraction. Just don't let your wars drag on, and if you don't find yourself at war very often, attack someone small, fight a couple of battles, and call a truce (maybe throw in a little gold if the AI is being its usual stubborn self

)
4) A good counter to beating the populists is trying to steal their less radical followers (political conviction less than 20) by giving them the job they want (for as little time as possible). this is the ONE AND ONLY time you should consider giving a populist an important job
5) Another way to beat the populists back is to have one faction dominate the senate. Personally, as the 'military republic' romans, por ejemplo, i only let military guys in, but other govt's work with the other parties (they all have good bonuses in my opinion) Basically, just give all the jobs to one political party, occasionally using point no. 4) to win over the senators from other parties who are sitting-on-the-fence.
6) Finally, watch out for people with no titles at all (who aren't massively populist) and give them something to do! particularly with young people you need to pay attention to their political situation, they are the govt. of tomorrow. younglings in your majority party should be particularly taken well care of (make sure jobs are rotated so these guys get known and start moving in the right circles

)
Sorry this was so long

but i kept thinking of things to add...
Thanks for reading! {thumbs up}