Black has a lot of choices because c3 doesn't put immediate pressure on black.
RJ's 3. ... Bc5 may be one of the worst, because it plays right into white's hands (losing time in the process).
I have tried many moves against the Ponziani over the years.
3. ... d5
This is a theoritical line. I believe that it is the recommendation in the Emms book Play The Open Games As Black. Black must learn to meet exd5, Bb5, and Qa4. Black doesn't have any real problems, but I personally didn't like the positions it led to as much.
3. ... Nf6
This is the other main recommendation (including by Marin in his book on 1. ...e5).
3. ... Nf6 can lead to closed positional maneuvering, but there are chances for black. Marin introduced an interesting variation where black gets an open h file (and all sorts of Rh4 ideas pop up for black.)
I think it goes like this:
I have tried more rare variations against the Ponziani too.
3. ... f5
When I want the initiative or an attempt at a quick win, I go for f5. It's like a Latvian Gambit where c3 doesn't really help white. White may get an edge, theoretically, but it's a good fighting move.
This is good for a good closed battle as well. 4.Bb5 can go into a Ruy Lopez Steinitz (but with a pawn on c3). With d6, black just plays a solid move and leaves most of theory. With patient play, black will get chances to outplay white in the late middlegame or endgame. 4.d4 Bd7 is usually how I follow up.
Bd7 just keeps the queens on, so that black can have more chances later.
I imagine 3. ... Qe7
would also be playable. Black follows up with g6. The good thing is that white no longer has Nc3 and Nd5.
The Ponziani just lets up the pressure to early, to lead to a forced advantage in my opinion.