Many games, especially ancient ones, have their own set of manners. For instance, Go players bow before the game and greet each other ("onegaishimasu") and play the first stone in the upper right corner [etc]. Is there something similar in mahjong, too?
Mahjong (actually Majiang - 麻将 in mandarin) is really just played like a card game. It's mainly played in China and doesn't have the "manners" that you can find in Japanese traditions.
Old people play mahjong like they would play a card game, some people play for money, but there are no manners to follow others than the rules of the game.
In addition to the insight given by repecmps, I'd like to add this link. It points out a few common sense ideas about politeness in games, and also has notes on tournament play. This is not exactly "manners", but I guess it's related.