E. I. du Pont de Nemours & Co.'s second-quarter earnings dropped 39 percent and for the first six months of this year, earnings plunged 59 percent compared with the same period in 1984, the Wilmington, Del.-based firm announced yesterday.

In other earnings reports yesterday:

General Foods Corp. said its profit fell 30.5 percent in the first quarter of its fiscal 1986 year from the same period a year earlier, which included an unusual gain from the sale of its Gaines pet foods business.

Goodyear Tire & Rubber Co. said 1985 second-quarter sales declined 2.2 percent, resulting in a 20 percent drop in net earnings, to $86.7 million.

Continental Airlines, continuing to operate under the protection of a federal bankruptcy court, reported the highest revenue and net income for any quarter and six-month period in the company's 50-year history.

Chris-Craft Industries Inc. reported a profit of $5.33 million in the second quarter vs. a $16.97 million loss in the same period last year.

Anheuser-Busch Cos. Inc. said its second-quarter profit rose 15 percent from a year earlier on a 7.7 percent sales gain.

Diamond Shamrock Corp. reported a $764.4 million loss in the second quarter because of a previously announced reorganization of the energy company that included writing down the value of its assets by $810.3 million.

*Du Pont Co.'s second-quarter net income was reported at $268 million, down from a record $437 million earned in the second quarter of last year.

Earnings per share were $1.10 for the second quarter, compared with $1.81 per share for the same quarter in 1984.

Sales for the second quarter were $8.5 billion, a 6 percent drop from the $9.1 billion in sales recorded for the quarter the previous year.

For the first six months, net income was $332 million, a 59 percent drop from the $810 million reported in the same period of 1984.

Earnings per share for the first six months were $1.36, compared with $3.36 for the first six months last year.

Sales were $16.8 billion, down 9 percent from the $18.4 billion in the first half of 1984.

"The reduced earnings reflect continued weakness in the industrial sector of the domestic economy, which has experienced virtually no growth since the middle of 1984," said Edward G. Jefferson, Du Pont chairman.

"In addition, the abnormally strong dollar has further eroded prices and volume in domestic markets, which are flooded with imports, and in international markets where the cost competitiveness of our exports has been severely impaired," he said.

The company said the agricultural and industrial chemicals, fibers and polymer products segments accounted for most of the overall decline in earnings from the second quarter of last year.

*General Foods, which is based in White Plains, N.Y., said net income for the three months ended June 29 totaled $77.6 million ($1.65 a share), compared with $111.6 million ($2.17) a year earlier.

Earnings from continuing operations rose 7.2 percent, it said.

Revenue edged up 0.4 percent to $2.27 billion from $2.26 billion, it said.

Last year's first-quarter results included a gain of $98.3 million from the Gaines sale and a $21 million loss from the restructuring of some operations, it said.

*For the second quarter, Goodyear Tire & Rubber Co.'s earnings were $86.7 million (81 cents per share) on sales of $2.57 billion, compared with earnings of $108.6 million ($1.02), on sales of $2.63 billion for the same period in 1984.

Robert E. Mercer, chairman and chief executive officer of the Akron, Ohio-based company, attributed the second-quarter results to a lower demand for private brand replacement tires in the United States, a glut of imported tires in the U.S. market and the eroding effect of the strong U.S. dollar on foreign sales as reported in U.S. dollars.

For the first half of 1985, the company's sales dropped 2.2 percent to $5.03 billion and earnings declined 21.3 percent to $173.4 million, compared with sales of $5.14 billion and earnings of $220.4 million for the first six months of 1984.

First-half earnings per share dropped to $1.62 from $2.08.

Mercer said unit sales of Goodyear brand replacement auto tires edged up, and demand from U.S. auto makers for the company's tires continued strong. He said other automotive products such as wheels, hose and belts benefited from a strong demand for original equipment.

*Continental Airlines' net income for the three months ended June 30 increased 341 percent to $35.4 million ($1.24 a share) on 53.8 percent higher revenue of $432.5 million. It was the fifth consecutive quarter in which Continental reported a net profit.

In the comparable period a year ago, Continental reported net income of $10.4 million (40 cents a share) on operating revenue of $281.5 million.

Continental's net income for the first six months of 1985 increased almost tenfold, to $50.4 million ($1.79), compared with $5.5 million (12 cents) for the first half of 1984. Revenue for the six months ended June 30 rose 59.5 percent to $795.6 million from $498.9 million in the same period last year.

"The company is growing stronger, operationally as well as profitably," said Continental Chairman Frank Lorenzo.

Continental filed for reorganization under federal bankruptcy statutes in September 1983. Before its reorganization, the carrier lost more than $218 million in 1983.

The airline continues operating under Chapter 11, but has advised a federal bankruptcy court it will submit a reorganization plan by Sept. 5, said spokesman Mike Cinelli. New York-based Chris-Craft Industries Inc., which recently changed its fiscal year end to Dec. 31 from Aug. 31, earned 75 cents a share in the latest quarter. Revenue climbed to $51.21 million from $46.87 million in the same period last year.

Chris-Craft attributed the earnings gain primarily to higher profits from BHC Inc., its majority-owned television broadcasting subsidiary.

"BHC's flagship station, KCOP in Los Angeles, had another outstanding quarter, while total income for BHC's six stations was about the same as for last year's corresponding period," said Chris-Craft Chairman Herbert J. Siegel.

He pointed out that BHC's earnings rose sharply as income associated with its 42.5 percent ownership in Warner Communications Inc. increased to $4.94 million from a loss of $72,000 in the year-ago quarter.

For the first six months Chris-Craft had net earnings of $3.85 million (39 cents a share), in contrast to a loss of $15.75 million in the same period last year. Six-month revenue increased to $89.57 million from $80.62 million. St. Louis-based Anheuser-Busch, the nation's largest brewer, said net income climbed to $130.4 million (83 cents a share), from $113.4 million (71 cents) a year earlier. The earnings per share reflect a 3-for-1 stock split on June 14, the company said.

Second-quarter sales rose to $2.01 billion from $1.87 billion.

Anheuser-Busch, whose beers include Budweiser, Michelob and Busch, said second-quarter beer shipments rose 6.5 percent to 18.2 million barrels from 17.1 million a year ago.

However, the company said earnings and volume growth rates for the second half of 1985 would trail those of the first six months because of an inventory buildup program in the first half of the year.

In the first half of 1985, Anheuser-Busch's profit rose 15.6 percent to $220.9 million ($1.41), from $191 million ($1.20) a year earlier. Six-month sales climbed to $3.82 billion from $3.49 billion.

*Dallas-based Diamond Shamrock Corp. said that, without the unusual charge, earnings in the quarter would have been $45.9 million (33 cents a share), compared with $64.3 million (48 cents) a year earlier. Revenue declined to $1 billion from $1.1 billion.

The writedown is also expected to mean the company will show a loss for the entire year, said William Bricker, the chairman of Diamond Shamrock.

Diamond Shamrock said it lost $705.3 million ($5.72) for the first six months of 1985. For the similar period last year, the company earned $123.8 million (91 cents). Revenue for the first six months was $2 billion, down from $2.3 billion for the first half of 1984.