Reciprocity: People tend to return favors.
The best way to get help is to give it first.
When you play a show for a new promoter, print up fliers with your own money and pass them around, making sure that the promoter knows you were the one who did it. Then talk to them after the show and ask "Hey, can you guys put us on with the next national act that comes though?" Not only does the promoter know you'll help them do their job and thus make more money, there's the social obligation to pay back those who help you. Don't underestimate this effect.