While reading an article at http://www.reuters.com/article/2012/03/19/us-usa-economy-stockton-idUSBRE82I0EJ20120319?feedType=... , there is "buy-generic cousin" in the first paragraph, and would somebody help to make me understand the meaning of it?

The general tone of the article personifies Stockton as an unfashionable, unsophisticated person ( commonly called 'a country cousin'). Such a person wears polyester clothes, and buys generic items instead of popular and more expensive brands.

It's a very informal way to say that Stockton is a less than first rate town.

First, "cousin" is of course a relative, specifically your cousin is your parent's sibling's child. In U.S. culture this is considered a somewhat distant relationship.
Second, "buy-generic" is meant to be a disparaging term for those who buy generic (not brand name) products to save money. The implication being that they are too poor to buy brand name products.

So, to refer to Stockton as a "buy-generic cousin" is to say that it is a poor town that is not really very well regarded.