I think playing as that character has a better chance of getting items related to them. It was like that in PW1, and I think it's the same as PW2, so play as Law. Might should play on Easy too, to make sure you get bronze coins.
And I can't remember the name off the top of my head, but I'm sure there's got to be some item in the shop you can get that increases chance of getting coins with marks, so buy that.
Here's everything you can do to increase your odds to get this coin:
- Check in the Gallery in which categories the coin you want shows up. I'm sure Laws Mark shows up in several categories. Look for the one with the fewest entries overall. - Find a stage that drops this categorie. (Stage select, toggle view with L/R trigger) - Select the lowest stage you can find and enter the shop from there to buy a Map of the category you need. - Play the stage... on Easy, with a recommended character (thumbs up). I'm not sure if the characters level does anything to help getting bronze coins only, but it can't hurt to pick a high-level character... - Open every single treasure chest in that stage. - Kill every named and unnamed enemy commander (most unnamed commanders will only drop items, but I've had them drop coins sometimes, too... and since it's not hard to kill them on Easy, it's worth a try) - Meet the conditions for the secret coins to appear.... and open that chests, of course.
You should get tons of coins after that stage, and most of them should be of the category you chose. So the fewer entries this category has, the higher the chance to get this one, elusive coin. Good Luck. :-)