Two of the nation's major retailers, Sears, Roebuck & Co. and K mart Corp., reported vastly different earnings for the second quarter yesterday.

Still showing signs of its program to reduce promotional items, Sears, Roebuck & Co. said yesterday its profits declined 3.6 percent during the second quarter. Sales fell 5.3 percent in the quarter ended July 31.

The nation's largest retailer said net income was $193.6 million (60 cents per share), compared with $200.8 million (63 cents) in the same 1978 period.

Sales were $4.25 billion compared with $4.49 billion in the year-earlier period.

Net income for the first six months was $343.6 million ($1.07). This was 3.5 per cent lower than last year's six-month earnings of $356.2 million ($1.11).

First-half sales were $7.88 billion, down 7.9 percent from first-half 1978 volume of $8.56 billion.

Sears began a deliberate scaling down of its promotion program about one year ago to cut costs, but the move also has dampened its profitability in the past two quarters.

Spokesman Earnest Arms, said Sears has begun to increase it's promotions once again.

"We've just come around the horn," he said, "and now we're into a fine tuning kind of thing" with the level of promotions.

K mart's net income was $89.7 million (71 cents) compared with $81.1 million (65 cents) in the year-earlier quarter.

SecondQuarter sales reached $3.038 billion, compared with $2.77 billion in the second quarter of 1978.

"Sales for the second quarter of 1979 were within expectations despite weakening in the general economy," Chairman Robert E. Dewar said."Our merchandise plans for the remainder of the year have been made in anticipation of a less buoyant economy."

Sales for the six months ended Aug. 1 totaled $5.65 billion, a 16 percent increase above the $4.87 billion in sales in a comparable 1978 period.

Six-month earnings were $135 million lion($1.08) compared with $115 million (93 cents) in the first half of 1978.

Citing sluggish domestic tire sales, Firestone Tire & Rubber Co. announced its fiscal third quarter earnings fell 35 percent.

The firm earned $10.4 million (18 cents) in the quarter, compared with $15.9 million (27 cents) in the same period a year ago.

Third-quarter sales rose slightly to $1.3 billion, compared with $1.2 billion in the year-earlier quarter.

Chairman Richard A. Riley said third-quarter results were "adversely affected by sluggish domestic tire demand for the industry as a whole related to energy uncertainities.

For the fiscal year's first nine months, net income was $77.8 million ($1.35 a share), compared with $51.9 million (90 cents) for the same period last year, excluding the effect of a 1978 second-quarter write-off of $110 million to provide for losses related to phasing out tire production at some domestic and foreign plants. Sales for the nine months were $3.9 billion, compared with $3.5 billion in the first three quarters of last year.

Deere & Co., the maker of farm and industrial machinery, had a 17-percent gain in earnings in its third quarter ended July 31, the company announced yesterday. Per-share earnings were $1.60 against $1.38.

Net income was $97 million on sales of $1.408 billion against $83.1 million. The sales gain was 25 percent.

Nine month sales were up 21 percent at $3.672 billion and net income was $271 million ($4.47) against $219.9 million ($3.64) a year earlier.

Chairman William A. Hewitt said the gains occurred in spite of a drop in international sales and higher costs abroad. But Hewitt said he expected new products to overcome the problems in the international field. However, foreign exchange translation losses for the nine months were only $4.5 million against $23.7 million a year ago. See EARN, D9, Col. 1