The first piece they use to convince others to join them
is that Caesar is has too much power. They feel he has more power than he deserves. Everyone sees him as the savior of Rome and the poor. To the conspirators they see him as a threat. They feel he is going to ruin the government and take over Rome. Caesar won a battle and the conspirators feel like people are making it seem like he won the war.
The conspirators feel that Caesar is being treated like a god even though he is an average man. The conspirators tell people that he is weak and will never be a good ruler. They tell them that he will ruin everything. After the battle they give Caesar a parade to celebrate and the conspirators tell the citizens that only gods get parades and Caesar is only an average man.
The last reason that the conspirators tell people to join them is that Caesar was physically and emotionally weak. Antony offered to crown Caesar three times and he turned down the offer every time. Maybe it was because he could not handle the pressure of being in charge. Antony also says that during the celebration Caesar fell to the ground and started to have a seizure. The conspirators are telling the people that Caesar could physically not handle being in charge. They are saying that if he came to power he would die from the pressure.
The conspirators were obviously very good at persuasion because there plan worked, they killed Caesar. Even some of Caesars closest friends turned on him and helped with the murder. They then celebrated their kill in the city. So there power of persuasion was both logic and emotions, it made sense to them so they convinced everyone else that it was right as well.