Irving's satirical view of early American life through "The Devil and Tom Walker" uses the Walkers and townspeople to discuss greed's all-encompassing effects. If you consider marriage a social institution, then you could certainly argue that Tom and his termagant wife's marriage portrays greed. Each "partner" is more concerned about getting what he/she deserves; there is no willingness on either one's part to work together within their marriage to make it what it should be. The premise of your question is that the social institution itself encourages this type of behavior between Tom and his wife. While I don't agree with that--I think that Mr. and Mrs. Walker were most likely greedy individuals before they entered into marriage--you can certainly prove through the story that marriage caused them to strive even more for individual possessions rather than shared ones. Tom's wife wants him to sell his soul to the devil so that she can prosper; she doesn't care that she would lose her husband. Likewise, when Tom's wife disappears, he is more worried about the material possessions that also disappeared than he is about his own spouse.
Irving also satirizes religious societies and their hypocrisy. If Tom's townspeople were not greedy, wanting to spend more than they possessed, there would be no need for Tom's usury services. The whole idea of usury--lending money at high rates of interest--encourages greed in a twofold manner. Tom does not care if he ruins the lives of his fellow church members by charging such high interest, he simply wants to make as much money as possible. Moreover, his greedy customers want more money than they are able to make.
Another character besides the Walkers, Tom's clients, and Old Scratch who demonstrates greed is a wealthy man of the county, Crowninshield. When Tom first meets the devil in the forest, Crowninshield's tree has just been cut down (symbolizing his death), and Irving describes him in the following manner:
The [tree] on which he had been seated, and which had evidently just been hewn down, bore the name of Crowninshield; and he recollected a mighty rich man of that name, who made a vulgar display of wealth, which it was whispered he had acquired by buccaneering.
Irving implies that because Crowninshield's wealth was a result of greed he eventually loses his soul to the devil. Additionally, Tom sees Deacon Peabody's (a religious community member) name on one of the trees and argues with the devil about Peabody owning the trees. The fact that Peabody's name is on the tree, that the tree is scored by the devil, and that he has established such a reputation that people think that the forest is his, illustrates that Peobody will meet the same fate as Crowninshield because of his greed.
From this story, it would be difficult to argue that the church itself encourages greed, but you could infer that the superstitions and religious beliefs that many early Americans possessed encouraged them to be greedy. For example, because of Tom's superstitions, he carries around his Bible and buries his horse upside down so that he can hopefully escape before everything can be taken from him. Also, the churchgoers have become so caught up in obtaining more possessions that they judge one another while sinking deeper into greed themselves.