Sears, Roebuck and Co., the nation's largest retailer, reported yesterday that its third-quarter earnings fell 4.7 percent because of rising interest rates and declines in its insurance business.

The decline would have been worse without one-time gains of $50.4 million, primarily from the sale of two shopping centers. In the same period a year ago, the company's earnings included $8.8 million in similar net capital gains and other income.

Sears, which built its reputation through its department store and mail-order merchandising operations, now describes itself as "the diversified general merchandise, insurance, real estate and financial services company." It has said it wants to become the biggest financial-services company in the United States.

Earlier this month, Sears agreed to buy Coldwell Banker & Co., the nation's leading real-estate brokerage company, and announced it would acquire Dean Witter Reynolds Organization Inc., the fifth-largest investment house. It already owns the Allstate insurance business.

Sears reported earnings of $125.2 million (40 cents a share) compared with $131.4 million (42 cents) for the same three months of 1980. Last year's earnings were restated because Sears switched accounting methods and changed its financial reporting from a fiscal year ending Jan. 31 to a calendar year.

Third-quarter revenues rose 8.1 percent to $6.83 billion from $6.31 billion a year ago.

Nine-month profits increased 10.3 percent to $297.9 million (94 cents a share) from $270.1 million (86 cents) a year earlier. Revenues were $19.21 billion, a 9.5 percent increase from the $17.54 billion of last year.

Edward R. Telling, chairman and chief executive officer, said that although domestic merchandising sales and income were above expectations, higher interest expenses cut seriously into overall profits.

Merchandising income was $74.5 million for the third quarter compared with $22.5 million last year, he said. However, credit operations lost $27 million compared with a gain of $5.5 million a year ago.

The company also said underwriting earnings for its Allstate Group dropped from $114.6 million in the third quarter of 1980 to $80.1 million for the comparable period this year.

A weak economy and the effects of the air traffic controllers strike caused a sharp dip in third-quarter earnings for UAL Inc., parent company of United Airlines, the company said yesterday.

UAL's profits were $7.21 million (24 cents a share) compared with $15.65 million ( 53 cents) in the 1980 third quarter, the company said.

The company lost $5.46 million in the first nine months compared with an $11.42 million loss in the first three quarters of 1980.

UAL's president and chief executive officer, Richard J. Ferris, said slow hotel business contributed to the sluggish performance. UAL owns Westin hotels, Mauna Kea Properties and GAB Business Services in addition to United.

The airline lost $400,000 in the quarter compared with $5.1 million in earnings in the same period last year, operating revenues were up 2 percent to $1.22 billion, and operating expenses were up 1 percent to $1.20 billion.

Goodyear Tire & Rubber Co. reported yesterday that third-quarter earnings dropped 34.2 percent despite record sales, due largely to the poor economic conditions in Europe.

Goodyear earned $38.2 million (53 cents a share) compared with $58 million (80 cents) in the 1980 third quarter. Sales were $2.3 billion, up 8.3 percent from $2.1 billion last year.

Chairman Charles J. Pilliod cited increased auto and truck tire sales in the United States and stronger demand for general products as a factor in a 20.1 percent boost in domestic sales to $1.4 billion from $1.2 billion and an increase in domestic earnings to $58.3 million from $13.5 million for the 1980 quarter.

A $20.1 million foreign loss was recorded for the quarter compared with foreign earnings of $44.5 million for the 1980 period. Foreign sales for the quarter were $923.5 million, down 5.7 percent from $979.7 million during the 1980 quarter.

Nine-month earnings were $149.5 million ($2.06) compared with $151.8 million ($2.09) last year. Sales were $6.9 billion, up 10.8 percent from $6.3 billion last year.

Nine-month U.S. sales were up 19 percent to $4 billion from $3.4 billion last year. U.S. earnings rose to $137.7 million from $25.8 million.

Nine-month foreign sales were $2.9 billion compared with $2.8 billion last year. Earnings were $11.8 million, down from $126 million for the same period in 1980.

Coca-Cola Co. reported yesterday that its third-quarter earnings rose 42.8 percent from the same period in 1980.

Coca-Cola, the world's largest producer and distributor of soft drink syrups and concentrates, said net income totaled $146.6 million ($1.19 a share) compared with $102.6 million (83 cents) in the comparable 1980 quarter. Sales were $1.56 billion compared with $1.55 billion.

The Atlanta-based concern said its nine-month net income totaled $375.6 million ($3.04), up 15.1 percent from $326.3 million ($2.64) in the same period a year earlier. Sales rose to $4.59 billion from $4.31 billion.

The 1981 results included a $29 million net gain on the company's sale of Aqua-Chem Inc.

Coca-Cola Chairman Roberto C. Goizueta said the sales figures reflect increased unit sales of soft drinks and wine as well as higher prices for soft drink concentrate.

Sperry Corp. said yesterday that earnings plunged 60.8 percent in the quarter ended Sept. 30, and the maker of computers, aviation controls and machinery blamed high interest rates and the rising value of the dollar for the slide.

Earnings for the second quarter of Sperry's fiscal year fell to $30 million (72 cents a share) from $76.6 million ($1.89) in the same period of 1980. But revenues rose 1.6 percent to $1.29 billion from $1.27 billion a year ago.

Sperry estimated that the dollar's gains reduced earnings by 20 cents a fully diluted share in the second quarter compared with a 5-cent-a-share gain in the same 1980 period.

The total backlog of orders on Sept. 30 was $3.6 billion, up 8 percent from a year earlier. But the backlog of orders for Sperry New Holland farm equipment was off 29 percent.

Six-month earnings fell 67.1 percent to $45.8 million ($1.10) from $139.4 million ($3.45) a year earlier. But revenues rose 2.7 percent to $2.61 billion from $2.54 billion.

The New York Times Co. said yesterday that its third-quarter profits rose 28 percent from a year earlier.

The communications company said earnings were $10.2 million (82 cents a share) compared with $8 million (66 cents) in the similar period a year ago. Revenues were $205.6 million, up 19 percent from $172.7 million.

The company's newspapers--The New York Times and 18 smaller-city newspapers in the South--showed a 32 percent increase in operating profits to $9.9 million in the period ended Sept. 30 from $7.5 million a year ago.

For the year to date, the company reported net income of $36.4 million ($2.94), up 22 percent from $29.9 million ($2.48) a year ago. Revenues rose by 15 percent to $610.7 million from $530.9 million.