Hi Uriel,
A good, an often neglected anti-senate tactic, is to conquer more land away from where they set their missions. This makes them doubly frustrated, since the senate quite oddly begin to hate a faction should they begin gaining too much land.

As you have said, assassinations also can aid in the declaration of civil war, but they don't actually have any effect on the senate popularity rating. They just result in your faction being outlawed outright, as if you had attacked any province of another Roman, if your popular support is high enough (typically eight or more shields).

Hope this is useful, good luck!