As black I have enjoyed experimenting with 1. e4 e5 2. Nf3 b5. Of course 2...b5 is not good, but most opponents have spent a little time trying to decide which P to take.
If white plays 3. Bxb5 c6 where should he play his B? Surprisingly, most of my opponents (generally lower rated ones) have retreated it back which allows me to play 4...d5. 4.Ba4 is best.
Black can try either after 4...Ba6 or 4...Nf6. White is clearly better; if white now captures the e-Pawn black is still at a disadvantage, but he has a choice of either 5...Qa4 attacking two pieces or playing 5...Qe7. In either case white has the advantage, but against a tactically challenged opponent it can be very discombobulating.
Apparently white does best to capture the e-Pawn. Does this not makes sense? The center P is more important than a flank P. After 1. e4 e5 2. Nf3 b5 3. Nxe5 Qe7 4. d4
Black must avoid 4...d6 because of 5.Bxb5, but he can try either 4...Nc6 or 4...f6. Neither move is really very good, but if black is overly concerned about that, then he should not play 2...b5. Admittedly, none of this stuff is good, but things generally get rather tactical and IF you are better at them than your opponent, you'll probably win; if not you won't. But, for us non-masters that's the case even if we were playing the Ruy Lopez or Najdorf Sicilian.
This game features a rather better opening that I have been messing around with and there doesn't seem to be a whole lot of theory on it. I Googled Bishop's Opening Ponziani Gambit and got nothing more than some games in various databases. It's a good line to make your own opening book on so you will be familiar with the main lines then give it a try.