Sales of drug-eluting stents for Johnson & Johnson’s Cordis Corp. dropped 31 percent in 2010, adding to the misery for the New Brunswick, N.J.-based medical products giant amid a welter of recalls for its over-the-counter medicine operation and the DePuy ASR hip implant.

How do you spell relief?

For Johnson & Johnson (NYSE:JNJ), which has been battered for months by a series of recalls involving its over-the-counter pharma products (including Rolaids), it’s not D-E-S.

Cordis Corp., the stent-making operation of the New Brunswick, N.J.-based medical products giant said sales were down 10 percent during the fourth quarter of 2010. The unit posted Q4 sales of $629 million, compared to $697 million during the same period last year. For the full year, Cordis pulled in $2.5 billion, a 4.7 percent slide from $2.7 billion in 2009.

Drug-eluting stent sales, including Cordis’s flagship Cypher device, fell across the board during the quarter. Worldwide DES sales were $134 million, down 38 percent from $223 million during the 2009 fourth quarter.

The news wasn’t much better for the full year. J&J’s DES sales plunged 31 percent to $627 million, down from $919 million during 2009.

Company officials said the slumping DES sales were the result of “continued market and competitive pressures.” Cordis jostles for market position with other device mammoths including the vascular division of Abbott (NYSE:ABT), Medtronic Inc. (NYSE:MDT) and Boston Scientific Corp. (NYSE:DePuy ASR hip implant recall in August 2010.

JNJ’s constellation of recall woes took a big chunk out of overall fourth-quarter sales, which were down 5.5 percent to $15.6 billion, from $16.5 billion in Q4 2009. For the full year, sales were flat at $61.6 billion, down half a tick from $61.9 billion in 2009.

The bottom line was off about 12 percent during the fourth quarter, to $1.9 billion, or 70 cents per share, compared to $2.2 billion, or 79 cents a share, during Q4 2009.

Chairman and CEO William Wheldon warned investors on a conference that more recalls could come for its over-the-counter unit, as an internal audit unwinds.

“Most of it is behind of us,” Wheldon said. “But there could still be a little ahead of us.”

The company issued earnings guidance for full-year 2011 of $4.80 to $4.90 per share, lower than analysts’ consensus of $4.97. JNJ shares were down about 2 percent in mid-day trading.