What arguments did Antony use to convince the audience that Caesar was not ambitious in Julius Caesar?

Antony told the audience that Caesar loved them and left them money.

In Antony’s famous funeral oration, he whips the crowd into a frenzy.  His main objective is to convince them that Brutus and the other conspirators are murderers and not liberators.  In order to do this, he has to counter Brutus’s characterization of Caesar as a tyrant.

Because Brutus spoke first, Antony does have an advantage.  He can use Brutus’s words against him.  Brutus made himself out to be a tyrant-killer, telling the audience that they were living as slaves under Caesar.  Antony is aware that some in the audience will be suspicious of what he has to say, so he begins by telling them that he is not dismissing Caesar’s negative qualities. 

I come to bury Caesar, not to praise him.
The evil that men do lives after them;
The good is oft interred with their bones;
So let it be with Caesar. (Act 3, Scene 2)

This statement might have caught some of the audience off guard.  They would have expected to be hearing how great Caesar was from his head crony.  Instead, Antony uses the speech to attack Brutus and the others.  He tells them that if Caesar was ambitious, then he certainly paid for it.

Antony then reframes the conversation, reminding the people of Rome that Caesar made them rich.

He was my friend, faithful and just to me:
But Brutus says he was ambitious;
And Brutus is an honourable man.
He hath brought many captives home to Rome
Whose ransoms did the general coffers fill:
Did this in Caesar seem ambitious? (Act 3, 2)

This is very clever.  Antony is slowly turning the people against Brutus while not actively speaking against him.  By continually referring to Brutus and the others as honorable, he is making the people question that honor.  Antony clearly does not believe that there was anything honorable in what they did.

Antony points out where each conspirator stabbed Caesar.  He is painting them as murderers.  He also positions himself as Caesar’s heir, showing the audience Caesar’s will and telling them how generous he was to them.  Caesar not only made Rome rich, he is making each of them rich.  It shows how much Caesar loved the people of Rome.

It works.  Soon the crowd has not only forgiven Caesar, they have also remembered why he was so popular.  In a whirl of grief and anger, they attack the conspirators.  Antony has won the people over, and Brutus and the others are on the losing side.

Antony is the one who is being ambitious.  Well aware that Caesar's heir, Octavius, is on his way to Rome, Antony positions himself as the leader in Caesar's stead.  By telling the people about the will, he transferred their affection from Caesar to himself.