You'll want to concentrate on "short cons" -- things you can set up and follow through on quickly.
In my opinion, you can't go far wrong with the Pigeon Drop, or any combination thereof (found money scam, fiddle game, lost dog con, etc.).
The rule in a con is that the mark has to believe that *he* is the one doing the conning. He has to believe that he is the one being sneaky, that he is the one getting something for more than it is worth, etc. Even better, he cheats you to get it, so when the blowoff happens, he has no recourse. He can't exactly go to the authorities and say "I tried to cheat this guy, but he turned around and cheated me even more!".
Hence the phrase "You can't cheat an honest man." In the best cons, the honest guy walks away from it before it starts, and the dishonest guy tries to get something for nothing, and ends up getting taken.
So the classic Pigeon Drop is a two man con. You can find a writeup on it here.
Pigeon Drop - Found Money Scam
You can substitute an object for the found money, and the second player acts to convince the Mark that the object is in actuality worth quite a bit of money (rare prized violin, rare purebred dog, etc.). So it goes something like this ...
a. Artie the con man befriends Mark the mark briefly. They find a lost fiddle. It might be valuable. They agree that they've both found it, they both own it, but what to do with it? Artie must leave soon, so how to best make good on their find?
b. Artie leaves momentarily, and Bob the con man approaches, and notices Mark with the fiddle. He is astounded at the remarkably good condition of this prized fiddle, and says it is worth a substantial amount of money. How lucky Mark is to have found this amazingly expensive fiddle! Bob leaves.
c. Artie returns, and is in a hurry to go. He wants to pawn the fiddle for a paltry sum. Now, Mark is greedy, and knows that the fiddle is actually quite valuable. He doesn't tell Artie, though. Instead, Mark suggests that he buys Artie's half of the found fiddle for a substantial amount (but not nearly as much as it is really worth!). Artie is surprised, but 'reluctantly' agrees to take Mark's money, and gratefully departs.
d. When Mark goes to sell the fiddle, he discovers that it is a useless piece of junk, instead of the expensive work of art he was told.
e. Artie and Bob meet up and split the money that Mark freely gave them.
Remember -- Mark tried to cheat Artie! He can't very well go to the authorities and claim that he was swindled, 'cause he himself attempted to swindle poor Artie by buying his half of the fiddle so cheaply, believing it to be expensive.
You can do the same con with a lost dog (where Mark is convinced that it is a rare and expensive breed which anybody would gladly pay a handsome reward for!) or any other piece of "collectible" art.