Generally, it is harder for companies to become counter-cyclical, because it is fairly difficult to find a business model that thrives in a period where most people do not have money.
Outplacement agency stocks, for example, would be considered counter-cyclical, because these companies help laid-off workers find jobs in exchange for a fee. This type of company would be more successful during times of recession, because there would be more unemployed workers at that point in time compared to times of expansion.
Purchasing counter-cyclical stocks can serve as a good hedge to the standard recessionary pressures that can cause most stocks to decline.